]>
TErminology for the Description of DYnamics (TEDDY)
http://biomodels.net/teddy
http://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/tags/rel-2011-08-30/teddy.owl
rel-2014-04-24
The TErminology for the Description of DYnamics (TEDDY) project aims to provide an ontology for dynamical behaviours, observable dynamical phenomena, and control elements of bio-models and biological systems in Systems Biology and Synthetic Biology.
en
dependsOn
Relates temporal behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083] to functional motifs [http://identifiers.org/biomodels.teddy/TEDDY_0000003] they depend on.
hasFeature
Links a dynamic system to the way one or several temporal behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083] are modified or related upon interaction with information external to the system considered.
hasCharacteristic
Used to describe properties by means of behaviour characteristic [http://identifiers.org/biomodels.teddy/TEDDY_0000002].
hasSubPart
true
hasSuperPart
true
hasOnPart
true
adjacentTo
Two temporal behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083] are adjacentTo each other if and only if they are in phase space proximity.
convergeTo
A temporal behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] convergeTo another temporal behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] if and only if it reaches the other behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] as time goes to either positive or negative infinity.
reverseOf
reverseOf links two temporal behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083] whose phase diagrams can be obtained from each other by reversing the directions of all the phase paths.
transforms
true
below
Links a bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000053] to a 'temporal behaviour' [http://identifiers.org/biomodels.teddy/TEDDY_0000083] which exists below the critical value of the bifurcation parameter.
above
Links a bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000053] to a 'temporal behaviour' [http://identifiers.org/biomodels.teddy/TEDDY_0000083] which exists above the critical value of the bifurcation parameter.
hasPart
Inverse of partOf [obo:part_of].
partOf
http://obofoundry.org/ro/#OBO_REL:part_of
For continuants: C part_of C* if and only if: given any c that instantiates C at a time t, there is some c* such that c* instantiates C* at time t, and c part_of c* at t.
For processes: P part_of P* if and only if: given any p that instantiates P at a time t, there is some p* such that p* instantiates P* at time t, and p part_of p* at t. (Here part_of is the instance-level part-relation.)
hasValue
Links a 'behaviour characteristic' [http://identifiers.org/biomodels.teddy/TEDDY_0000002] to the type of its value.
TEDDY entity
A Thing related to the dynamics of bio-models and biological systems. Terms belonging to TEDDY Entities are used in descriptions of dynamical behaviours, observable dynamical phenomena, and control elements in Systems Biology and Synthetic Biology.
curve ((obsolete))
true
Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'.
behaviour characteristic
Behaviour characteristic is a property that characterizes temporal behaviors [http://identifiers.org/biomodels.teddy/TEDDY_0000083].
functional motif
http://identifiers.org/doi/10.1371/journal.pbio.0020369
A connected graph or network consisting of M vertices and a set of edges having a particular functional significance, forming a subgraph of a larger network.
http://identifiers.org/doi/10.1371/journal.pbio.0020369
Sporns O, Kötter R (2004) Motifs in Brain Networks, PLoS Biology, 2(11):e369.
monotonicity
http://mathworld.wolfram.com/MonotonicFunction.html
A curve is `monotonic` if successive states are ordered either entirely non-decreasing or entirely non-increasing.
monotone
monotonic
http://mathworld.wolfram.com/MonotonicFunction.html
Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource.
non-monotonic
http://mathworld.wolfram.com/MonotonicFunction.html
A curve is non-monotonic if it has both increasing ordered successive states and decreasing orderd succesive states.
http://mathworld.wolfram.com/MonotonicFunction.html
Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource.
oscillation
http://mathworld.wolfram.com/Oscillation.html
The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge.
http://mathworld.wolfram.com/Oscillation.html
Weisstein, Eric W. Oscillation. From MathWorld--A Wolfram Web Resource.
strict monotonicity
http://eom.springer.de/M/m064830.htm
A curve is strictly monotonic if it is monotonic [http://identifiers.org/biomodels.teddy/TEDDY_0000004] and has no equal temporal successive states.
strictly monotone
strictly monotonic
http://eom.springer.de/M/m064830.htm
Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource.
strictly increasing
http://eom.springer.de/M/m064830.htm
A curve is strictly increasing if it is strictly monotonic [http://identifiers.org/biomodels.teddy/TEDDY_0000007] with temporal successive states increasing ordered.
isotonic
http://eom.springer.de/M/m064830.htm
Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource.
strictly decreasing
http://eom.springer.de/M/m064830.htm
A curve is strictly decreasing if it is strictly monotonic [http://identifiers.org/biomodels.teddy/TEDDY_0000007] with temporal successive states decreasing ordered.
antitonic
http://eom.springer.de/M/m064830.htm
Weisstein, Eric W. Monotonic Function. From MathWorld--A Wolfram Web Resource.
single turnaround
A trajectory [http://identifiers.org/biomodels.teddy/TEDDY_0000083] of the system which responds negatively to displacement from equilbrium [http://identifiers.org/biomodels.teddy/TEDDY_0000086]: moving away from equilibrium the trajectory turns around and moves back towards equilibrium.
steady state ((obsolete))
true
Obsolete: equivalent to TEDDY_0000086 'Fixed Point'.
rate of change
The rate of growth/decay.
linear rate of change
http://identifiers.org/isbn/1844071448
A quantity changes linearly when its change is a constant amount over a given period of time.
http://identifiers.org/isbn/1844071448
D. H. Meadows (2005) The Limits to Growth: The 30-Year Update, Rff Press, revised ed.
exponential rate of change
http://identifiers.org/isbn/1844071448
A quantity changes exponentially when its change over a given period of time is proportional to what is already there.
http://identifiers.org/isbn/1844071448
D. H. Meadows (2005) The Limits to Growth: The 30-Year Update, Rff Press, revised ed.
curve shape
Characteristic describing the shape of the graph of a function.
concave shape
http://identifiers.org/isbn/0691080690
A shape of a graph of a concave function, i.e. a function whose negative is convex [http://identifiers.org/biomodels.teddy/TEDDY_0000021].
http://identifiers.org/isbn/0691080690
R. T. Rockafellar (1970) Convex Analysis (Princeton Mathematical Series), Princeton Univ Pr. (p.23)
zero rate of change
http://identifiers.org/isbn/1844071448
A quantity has a zero rate of change when it neither grows nor declines.
http://identifiers.org/isbn/1844071448
D. H. Meadows (2005) The Limits to Growth: The 30-Year Update, Rff Press, revised ed.
polynomial rate of change
A quantity changes polynomially when its change function is bounded above by a polinomial function.
power rate of change
linear increasing
A curve is linear increasing if it is is strictly increasing with a linear rate of change.
linear decreasing
A curve is linear decreasing if it is is strictly decreasing with a linear rate of change.
convex shape
http://identifiers.org/isbn/0691080690
A shape of a graph of a convex function, i.e. a function whose epigraph (the set of points on or above the graph of the function) is a convex as a subset of R^n. A subset G of a linear space is said to be convex, if it contains the whole segment (closed straight line segment) joining each of its two points.
http://identifiers.org/isbn/0691080690
R. T. Rockafellar (1970) Convex Analysis (Princeton Mathematical Series), Princeton Univ Pr. (p.10, 23)
straight line shape
A shape of a graph of a linear function.
curve characteristic
A characteristic of the 'temporal behaviour' [http://identifiers.org/biomodels.teddy/TEDDY_0000083] curve (projection of the function graph onto a single variable).
unbounded growth ((obsolete))
true
limit
http://eom.springer.de/L/l058820.htm
One of the fundamental concepts in mathematics, meaning that a variable depending on another variable arbitrary closely approaches some constant as the latter variable changes in a definite manner.
http://eom.springer.de/L/l058820.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
asymptotic limit
http://eom.springer.de/a/a012870.htm
A limit of a function f(x) as x->x0 over a set E for which x0 is a density point.
approximate limit
http://eom.springer.de/a/a012870.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
asymptotic upper limit
http://eom.springer.de/a/a012870.htm
An approximate upper limit of a function f(x) at a point x0 is the lower bound of the set of numbers y (including y=positive infinity) for which x0 is a point of dispersion of the set {x: f(x)>y}.
approximate upper limit
http://eom.springer.de/a/a012870.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
asymptotic lower limit
http://eom.springer.de/a/a012870.htm
An approximate lower limit of a function f(x) at a point x0 is the upper bound of the set of numbers y (including y=negative infinity) for which x0 is a point of dispersion of the set {x: f(x)<y}.
approximate lower limit
http://eom.springer.de/a/a012870.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
plus infinity limit
http://eom.springer.de/I/i050930.htm
A function of x approaches plus infinity if its value becomes and remains larger than any given number as a result of variation of x.
http://eom.springer.de/I/i050930.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
infinite limit
http://eom.springer.de/I/i050930.htm
A function of a variable x has an infinite limit if its absolute value becomes and remains larger than any given number as a result of variation of x.
http://eom.springer.de/I/i050930.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
minus infinity limit
http://eom.springer.de/I/i050930.htm
A function of x approaches minus infinity if its value becomes and remains smaller than any given number as a result of variation of x.
http://eom.springer.de/I/i050930.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
sigmoid shape
http://identifiers.org/isbn/3540605053
A shape of a graph of a sigmoid function, i.e. a real function sc: R->(0,1) defined by the expression sc(x) = 1/(1 + e^(-cx)).
http://identifiers.org/isbn/3540605053
R. Rojas (1996) Neural Networks: A Systematic Introduction, Springer, 1st ed. (p.149)
feedback loop
http://identifiers.org/isbn/1584886420
A process whereby some proportion of function of the output signal of a system is passed (fed back) to the input.
feedback
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.266)
http://identifiers.org/isbn/1584886420
negative feedback loop
http://identifiers.org/doi/10.1016/j.febslet.2005.02.008
A component or variable of a system is subject to negative feedback when it inhibits its own level of activity.
negative feedback
http://identifiers.org/doi/10.1016/j.febslet.2005.02.008
Wolkenhauer O, Ullah M, Wellstead P, Cho K-H (2005) The dynamic systems approach to control and regulation of intracellular networks, FEBS Letters, 579 (8): 1846-1853.
positive feedback loop
http://identifiers.org/doi/10.1016/j.febslet.2005.02.008
A component or variable of a system is subject to positive feedback when it increases its own level of activity.
positive feedback
http://identifiers.org/doi/10.1016/j.febslet.2005.02.008
Wolkenhauer O, Ullah M, Wellstead P, Cho K-H (2005) The dynamic systems approach to control and regulation of intracellular networks, FEBS Letters, 579 (8): 1846-1853.
feed-forward loop
A 'three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000037] or its topological generalization.
FFL
feed-forward
feedforward
feedforward loop
three-node feed-forward loop
http://identifiers.org/isbn/1584886420
3-node FFL
3-node feed-forward
3-node feed-forward loop
3-node feedforward
3-node feedforward loop
A pattern with three nodes, X, Y, and Z, in which X has a directed edge to Y and Z, and Y has a directed edge to Z. The FFL is a network motif in many biological networks, and can perform a variety of tasks (such as sign-sensitive delay, sign-sensitive acceleration, and pulse generation).
FFL
thre-node FFL
three-node feedforward loop
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.267)
http://identifiers.org/isbn/1584886420
FFL
http://identifiers.org/isbn/1584886420 (p.41)
coherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
A feed-forward loop [http://identifiers.org/biomodels.teddy/TEDDY_0000037] in which the sign of the direct path from X to Z is the same as the overall sign of the indirect path from X through Y to Z.
coherent 3-node feed-forward loop
coherent 3-node feedforward
coherent 3-node feedforward loop
coherent three-node feedforward loop
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.265)
type-1 coherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
A 'coherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000038] in which all three regulations are positive.
C1-FFL
coherent 3-node feedforward type-1
type-1 coherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
type-2 coherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
A 'coherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000038] in which X represses Z, and also represses an activator of Z.
C2-FFL
coherent 3-node feedforward type-2
type-2 coherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
type-3 coherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
A 'coherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000038] in which X represses Z, and also activates a repressor of Z.
C3-FFL
coherent 3-node feedforward type-3
type-3 coherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
type-4 coherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
A 'coherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000038] in which X activates Z, and also represses a repressor of Z.
C4-FFL
coherent 3-node feedforward type-4
type-4 coherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
incoherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
A feed-forward loop [http://identifiers.org/biomodels.teddy/TEDDY_0000037] in which the sign of the direct path from X to Z is the opposite as the overall sign of the indirect path from X through Y to Z.
incoherent 3-node feed-forward loop
incoherent 3-node feedforward
incoherent 3-node feedforward loop
incoherent three-node feedforward loop
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.267)
type-1 incoherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
An 'incoherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000043] in which X activates Z, and also activates a repressor of Z.
I1-FFL
incoherent 3-node feedforward type-1
type-1 incoherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
type-2 incoherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
An 'incoherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000043] in which X represses Z, and also represses a repressor of Z.
I2-FFL
incoherent 3-node feedforward type-2
type-2 incoherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
type-3 incoherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
An 'incoherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000043] in which X represses Z, and also activates an activator of Z.
I3-FFL
incoherent 3-node feedforward type-3
type-3 incoherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
type-4 incoherent three-node feed-forward loop
http://identifiers.org/isbn/1584886420
An 'incoherent three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000043] in which X activates Z, and also represses an activator of Z.
I4-FFL
incoherent 3-node feedforward type-4
type-4 incoherent FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.47)
orbit ((obsolete))
true
Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'.
fixed point ((obsolete))
true
Obsolete: equivalent to TEDDY_0000086 'Fixed Point'.
periodic orbit
http://identifiers.org/isbn/0387983821
A temporal behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] which repeats every state after a specific period of time.
closed orbit
cycle
periodic solution
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.9)
limit cycle
http://identifiers.org/isbn/0738204536
Grenzzyklus
A closed orbit which is isolated, i.e. neighbouring orbits are not closed.
isolated closed path
http://identifiers.org/isbn/3817112823
Grenzzyklus
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196)
http://identifiers.org/isbn/0198565623 (p.30)
isolated closed path
parameter dependency ((obsolete))
true
Obsolete: not required anymore.
bifurcation
http://identifiers.org/isbn/0198565623
http://www.egwald.com/nonlineardynamics/bifurcations.php
A `characteristic` describing a sudden qualitative (topological) change in the orbit structure of a system occuring as a parameter passes through a critical value, called a bifurcation point.
http://www.egwald.com/nonlineardynamics/bifurcations.php
Elmer G. Wiens: Egwald Web Services Ltd.
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.420)
strange attractor
http://identifiers.org/isbn/0738204536
http://identifiers.org/isbn/9810221428
A non-periodic orbit [http://identifiers.org/biomodels.teddy/TEDDY_0000143] which is attracting and exhibits sensitive dependence on initial conditions.
The attractor [http://identifiers.org/biomodels.teddy/TEDDY_0000094] is strange if trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] on the attractor, being stable according to Poisson [http://identifiers.org/biomodels.teddy/TEDDY_0000149], are unstable according to Lyapunov [not TEDDY_0000113].
chaotic attractor
fractal attractor
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.325)
http://identifiers.org/isbn/9810221428
V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10)
http://identifiers.org/isbn/0738204536 (p.325)
chaotic attractor
http://identifiers.org/isbn/0738204536 (p.325)
fractal attractor
bursting
http://identifiers.org/isbn/0262090430
A burst is two or more spikes followed by a period of quiescence.
http://identifiers.org/isbn/0262090430
Izhikevich EM (2007) Dynamical systems in neuroscience : the geometry of excitability and bursting, MIT Press. (p.325)
switch
http://identifiers.org/doi/10.1371/journal.pcbi.1002085
A signaling network that converts a graded input cue into a binary, all-or-none response is said to exhibit ‘switch-like’ behavior; switching enables the establishment of discrete states which is vital in processes such as cell proliferation and differentiation.
http://identifiers.org/doi/10.1371/journal.pcbi.1002085
Shah NA, Sarkar CA (2011) Robust Network Topologies for Generating Switch-Like Cellular Responses, PLoS Comput Biol.; 7(6): e1002085.
stability ((obsolete))
true
Obsolete: not required anymore.
asymptotic decreasing ((obsolete))
http://eom.springer.de/A/a013610.htm
true
Asymptote of a curve y=f(x) with an infinite branch is a straight line the distance of which from the point (x, f(x)) on the curve tends to zero as the point moves along the branch of the curve to infinity. Decreasing function having for which an asymptote exists is called 'asymptotic decreasing'.
use 'strictly decreasing' [http://identifiers.org/biomodels.teddy/TEDDY_0000009] and 'asymptotic limit' [http://identifiers.org/biomodels.teddy/TEDDY_0000026] terms instead.
http://eom.springer.de/A/a013610.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
asymptotic increasing ((obsolete))
http://eom.springer.de/A/a013610.htm
true
Asymptote of a curve y=f(x) with an infinite branch is a straight line the distance of which from the point (x, f(x)) on the curve tends to zero as the point moves along the branch of the curve to infinity. Increasing function having for which an asymptote exists is called 'asymptotic increasing'.
use 'strictly increasing' [http://identifiers.org/biomodels.teddy/TEDDY_0000008] and 'asymptotic limit' [http://identifiers.org/biomodels.teddy/TEDDY_0000026] terms instead.
http://eom.springer.de/A/a013610.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
diverging increasing ((obsolete))
true
use 'strictly increasing' [http://identifiers.org/biomodels.teddy/TEDDY_0000008] and 'infinite limit' [http://identifiers.org/biomodels.teddy/TEDDY_0000030] terms instead.
chaotic oscillation
If a particular solution is aperiodic, but bounded for pt->infinity, then it corresponds to the regime of chaotic oscillation.
http://identifiers.org/isbn/9810221428
non-periodic oscillation
V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10)
http://identifiers.org/isbn/9810221428
sustained oscillation ((obsolete))
true
Obsolete: equivalent to TEDDY_0000051 'Limit Cycle'.
damped oscillation
http://identifiers.org/isbn/0486655083
Damping is any effect that tends to reduce the amplitude [http://identifiers.org/biomodels.teddy/TEDDY_0000131] of oscillations in an oscillatory system.
http://identifiers.org/isbn/0486655083
A. A. Andronov, A. A. Vitt, and S. E. Khaikin (1987) Theory of Oscillators, Dover Publications.
single-periodic oscillation
http://identifiers.org/isbn/0198565623
An oscillation [http://identifiers.org/biomodels.teddy/TEDDY_0000006] corresponding to a solution having a one-loop phase path and a period-1 Poincaré map.
SPO
single periodic oscillation
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.465)
mixed-mode oscillation
http://identifiers.org/doi/10.1063/1.2900015
MMO
Mixed-mode oscillations are complex periodic waveforms where each period is comprised of several maxima and minima of different amplitudes [http://identifiers.org/biomodels.teddy/TEDDY_0000131].
I. Erchova and D. J. McGonigle (2008) Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data, Chaos (Woodbury, N.Y.) 18.
mixed-mode oscillation
http://identifiers.org/doi/10.1063/1.2900015
I. Erchova & D. J. McGonigle (2008) Rhythms of the brain: an examination of mixed mode oscillation approaches to the analysis of neurophysiological data. Chaos (Woodbury, N.Y.) 18(1).
periodic oscillation
http://identifiers.org/isbn/9810221428
The characteristic of a periodic solution (a solution which is distinguished by the condition x*(t) = x*(t+T), where T is the period [http://identifiers.org/biomodels.teddy/TEDDY_0000067] of solution).
http://identifiers.org/isbn/9810221428
V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.6)
period
http://eom.springer.de/p/p072210.htm
For a periodic solution x(t), there is a number T, not equal to 0, such that x(t+T) = x(t) for t ∈ R. All possible such T are called periods of this periodic solution; the continuity of x(t) implies that either x(t) is independent of t or that all possible periods are integral multiples of one of them — the minimal period T0>0. When one speaks of a periodic solution, it is often understood that the second case applies, and T0 is simply termed the period.
http://eom.springer.de/p/p072210.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
regularity ((obsolete))
true
Obsolete: not required anymore.
local bifurcation
http://en.wikipedia.org/wiki/Bifurcation_theory#Local_bifurcations
http://identifiers.org/isbn/0387983821
A `bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000053] in which a stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133] fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] changes to an unstable [not TEDDY_0000133] one or vanishes. It can be detected within any small neighborhood of the fixed point: the real part of the eigenvalue of the linarisation around the fixed point is zero at the bifurcation.
bifurcation from steady state
bifurcation of equilibrium
bifurcation of equilibrium point
bifurcation of fixed point
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.58)
http://identifiers.org/isbn/0387983821 (p.58)
bifurcation of fixed point
http://identifiers.org/isbn/0387983821 (p.58)
bifurcation of equilibrium
http://www.scholarpedia.org/article/MATCONT
bifurcation from steady state
bifurcation of limit cycle
http://identifiers.org/isbn/0387983821
A global bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000147] in which a limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] (dis)appears or changes its stability [http://identifiers.org/biomodels.teddy/TEDDY_0000113].
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.162ff)
saddle-node bifurcation
1
1
1
1
http://identifiers.org/isbn/0387983821
http://identifiers.org/isbn/0738204536
A `zero-eigenvalue bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000123] in which a stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133] fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] and an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] collide and mutually annihilate.
blue sky bifurcation
fold bifurcation
limit point bifurcation
tangent bifurcation
turning-point bifurcation
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.45)
http://www.scholarpedia.org/article/Saddle-node_Bifurcation
limit point bifurcation
http://identifiers.org/isbn/0738204536 (p.47)
fold bifurcation
http://identifiers.org/isbn/0738204536 (p.47)
blue sky bifurcation
http://identifiers.org/isbn/0387983821 (p.80)
tangent bifurcation
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.80)
http://identifiers.org/isbn/0738204536 (p.47)
turning-point bifurcation
Hopf bifurcation
http://identifiers.org/isbn/0738204536
A `local bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000069] in which a `stable spiral` [http://identifiers.org/biomodels.teddy/TEDDY_0000126] changes in an `unstable spiral` [http://identifiers.org/biomodels.teddy/TEDDY_0000127]. The linearisation around the fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] has two conjugate eigenvalues. This eigenvalues cross simultaneously the imaginary axis from left (negative real part) to the right during the bifurcation.
Andronov-Hopf Bifurcation
http://identifiers.org/isbn/0387983821 (p.80)
Andronov-Hopf Bifurcation
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.248ff)
subcritical Hopf bifurcation
http://identifiers.org/isbn/0387983821
A `Hopf bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000072] in which an `unstable limit cycle` [http://identifiers.org/biomodels.teddy/TEDDY_0000128] is destroyed.
subc-AH
subcritical Andronov-Hopf bifurcation
http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
subcritical Andronov-Hopf bifurcation
http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
subc-AH
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.88)
supercritical Hopf bifurcation
http://identifiers.org/isbn/0738204536
A `Hopf bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000072] in which an `stable limit cycle` [http://identifiers.org/biomodels.teddy/TEDDY_0000114] appears.
supc-AH
supercritical Andronov-Hopf bifurcation
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.249)
http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
supc-AH
http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
supercritical Andronov-Hopf bifurcation
saddle-node on invariant circle bifurcation
http://identifiers.org/isbn/0262090430
SNIC
SNIC bifurcation
SNLC
SNLC bifurcation
Saddle-node bifurcation on invariant circle occurs when the center manifold of a saddle-node bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000071] forms an invariant circle. Such a bifurcation results in (dis)appearance of a limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] of an infinite period.
saddle-node on limit cycle bifurcation
http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle
SNLC bifurcation
http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle
SNLC
http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
SNIC
http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle
SNIC bifurcation
http://identifiers.org/isbn/0262090430
Izhikevich EM (2007) Dynamical systems in neuroscience : the geometry of excitability and bursting, MIT Press.
http://www.scholarpedia.org/article/Saddle-node_bifurcation_on_invariant_circle
saddle-node on limit cycle bifurcation
saddle-node bifurcation of limit cycles
2
0
http://identifiers.org/isbn/0387983821
A 'bifurcation of limit cycle' [http://identifiers.org/biomodels.teddy/TEDDY_0000070] in which two limit cycles [http://identifiers.org/biomodels.teddy/TEDDY_0000051] (stable [http://identifiers.org/biomodels.teddy/TEDDY_0000114] and saddle) collide and disappear.
fold bifurcation of limit cycles
http://identifiers.org/isbn/0387983821 (p. 163)
fold bifurcation of limit cycles
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.163)
period-doubling bifurcation of limit cycle
http://identifiers.org/isbn/0387983821
A 'bifurcation of limit cycle' [http://identifiers.org/biomodels.teddy/TEDDY_0000070] in which a 'periodic orbit' [http://identifiers.org/biomodels.teddy/TEDDY_0000050] with period-2 Poincaré map appears, while the fixed point changes its stability.
flip bifurcation of limit cycle
http://identifiers.org/isbn/0387983821 (p.163)
flip bifurcation of limit cycle
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.163)
Neimark-Sacker bifurcation of limit cycle
http://identifiers.org/isbn/0387983821
A 'bifurcation of limit cycle' [http://identifiers.org/biomodels.teddy/TEDDY_0000070] corresponding to the case when the multipliers are complex and simple and lie on the unit circle. The
Poincaré map then has a parameter-dependent, two-dimensional, invariant manifold on which a closed invariant curve generically bifurcates from the fixed point.
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.164)
integrator
_obsolete behaviour ((obsolete))
true
Obsolete: only one obsolete branch required.
_obsolete characteristic ((obsolete))
true
Obsolete: only one obsolete branch required.
_obsolete functionality ((obsolete))
true
Obsolete: only one obsolete branch required.
temporal behaviour
http://identifiers.org/isbn/0387983821
A temporal sequence of states following the evolution operator of the dynamical system through a given initial state.
orbit
phase curve
phase path
solution curve
trajectory
http://identifiers.org/isbn/0387983821 (p.8)
trajectory
http://identifiers.org/isbn/0198565623 (p.6)
phase path
http://identifiers.org/isbn/0387983821 (p.8)
orbit
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.8)
http://identifiers.org/isbn/0387908196 (p.2)
solution curve
parametrical behaviour ((obsolete))
true
Obsolete: not required anymore.
limit behaviour
http://identifiers.org/isbn/0387983821
A `temporal behaviour` [http://identifiers.org/biomodels.teddy/TEDDY_0000083] with all behaviours starting sufficiently near converge to it as time goes to either positive or negative infinity.
asymptotic state
limit set
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.10)
fixed point
http://mathworld.wolfram.com/FixedPoint.html
A 'temporal behaviour' [http://identifiers.org/biomodels.teddy/TEDDY_0000083] which does not change its state.
constant behaviour
constant solution
critical point
equilibrium
equilibrium point
equilibrium solution
rest solution
steady state
http://mathworld.wolfram.com/FixedPoint.html
Weisstein, Eric W. Fixed Point. From MathWorld--A Wolfram Web Resource.
http://identifiers.org/isbn/0198565623 (p.4)
equilibrium point
http://identifiers.org/isbn/0198565623 (p.4)
critical point
node
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] for which the Jacobian matrix has real-valued eigenvalues of the same sign.
fixed point node
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
center
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] for which the Jacobian matrix has purely imaginary complex conjugate eigenvalues. The fixed point is surrounded by a family of cycles in the phase portrait.
centre
elliptic fixed point
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137)
saddle
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] for which the Jacobian matrix has real-valued eigenvalues of opposite signs.
saddle point
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
http://identifiers.org/isbn/0198565623 (p.73)
saddle point
star
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] for which the Jacobian matrix has identical eigenvalues and two independent corresponding eigenvectors. All other trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] of the system lie on straight through the fixed point.
proper node
star point
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.135)
spiral
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] for which the Jacobian matrix has not purely imaginary complex conjugate eigenvalues. The fixed point is surrounded by spiralling behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083].
focus
spiral point
http://identifiers.org/isbn/0198565623 (p.73)
spiral point
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137)
http://identifiers.org/isbn/0198565623 (p.25)
focus
non-isolated fixed point
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] for which at least one eigenvalue of the Jacobian matrix is zero. If the other eigenvalue is non-zero the system has an entire line of fixed points along one dimension. If both eigenvalues are zero the system has a entire plane of fixed points.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.128,137)
degenerate node
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] for which the Jacobian matrix has identical eigenvalues and only one independent eigenvector. All other trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] of the system asymptotically become parallel to the unique eigendirection.
degenerated node
improper node
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.135f)
attractor
http://identifiers.org/isbn/0738204536
http://identifiers.org/isbn/9810221428
The limit set which corresponds to the particular type of stable solution and attracts phase trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] from a sertan region of initial conditions is an attractor.
http://identifiers.org/isbn/9810221428
V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10)
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.324)
Lyapunov stable fixed point
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] which is Liapunov stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133].
Liapunov stable fixed point
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129)
unstable ((obsolete))
http://identifiers.org/isbn/0738204536
true
Obsolete: a limit behaviour is unstable if it is neither Liapunov stable nor stable (use repellor instead).
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129)
asymptotic stability
http://identifiers.org/isbn/0738204536
A `stable behaviour` which is also a `Liapunov stable behaviour`.
The solution x*(t), t >= t0 is asymptotically stable, if all sufficiently small disturbances of the initial value lead to the solutions which re-approach the undisturbed solution.
stable behaviour
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129)
http://identifiers.org/isbn/0738204536, (p.129)
stable behaviour
neutral stability
http://identifiers.org/isbn/0738204536
A behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] which is Liapunov stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133] and not attracting [http://identifiers.org/biomodels.teddy/TEDDY_0000097].
asymptotically unstable
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129)
asymptotically unstable
http://identifiers.org/isbn/0198565623 (p.289)
saddle connection
1
2
http://identifiers.org/isbn/0738204536
A temporal behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] connecting two saddle points [http://identifiers.org/biomodels.teddy/TEDDY_0000089].
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.184)
homoclinic saddle connection
1
http://identifiers.org/isbn/0738204536
A saddle connection [http://identifiers.org/biomodels.teddy/TEDDY_0000099] connecting a saddle point [http://identifiers.org/biomodels.teddy/TEDDY_0000089] to itself.
homoclinic saddle loop
saddle loop
http://www.egwald.ca/nonlineardynamics/mathappendix.php#limitset
saddle loop
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.161)
http://identifiers.org/isbn/3540971416 (p.213)
homoclinic saddle loop
heteroclinic saddle connection
2
http://identifiers.org/isbn/0738204536
A saddle connection [http://identifiers.org/biomodels.teddy/TEDDY_0000099] connecting two different saddle points [http://identifiers.org/biomodels.teddy/TEDDY_0000089].
heteroclinic saddle trajectory
saddle connection
http://identifiers.org/isbn/0738204536 (p.166)
heteroclinic saddle trajectory
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.166)
http://identifiers.org/isbn/0738204536 (p.166)
The term `saddle connection` is used as a synonym for a heteroclinic orbit (http://identifiers.org/isbn/0738204536 (p.166) ). But `saddle connection` is also used for both: homoclinic and heteroclinic orbits (http://identifiers.org/isbn/0387943773 (p.184)).
saddle connection
repeller
http://eom.springer.de/R/r081310.htm
A subset of the phase space of the system that is an attractor [http://identifiers.org/biomodels.teddy/TEDDY_0000094] for the reverse [TR_0015] system.
repelling set
repellor
http://eom.springer.de/R/r081310.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
http://eom.springer.de/R/r081310.htm
repelling set
stable ((obsolete))
http://identifiers.org/isbn/0738204536
true
Obsolete: a limit behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000085] is stable if all behaviours starting sufficiently near to it will approach it as time goes to positive infinity (use attractor instead).
attracting
rdfs:label follows notation in http://identifiers.org/isbn/3817112823 (p.42).
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.128)
half-stable fixed point
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] which is half-stable [http://identifiers.org/biomodels.teddy/TEDDY_0000134], i.e. the fixed point is attracting in one direction and unstable in the other direction.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.26)
neutrally stable behaviour ((obsolete))
http://identifiers.org/isbn/0738204536
true
Non-Isolated Asymptotic Behaviour
Obsolete: a temporal behaviour which is neither attracting nor unstable (equivalent to 'neutrally stable' [http://identifiers.org/biomodels.teddy/TEDDY_0000098]).
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129)
non-isolated cycle
http://identifiers.org/isbn/0738204536
A cycle which is surrounded by other cycles.
neutrally stable cycle
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196)
temporal behaviour ((obsolete))
true
Obsolete: equivalent to TEDDY_0000083 'Temporal Behaviour'.
perturbation response
A response to perturbations of the system or its environment.
monostable perturbation response
http://identifiers.org/doi/10.1371/journal.pone.0021782
A `perturbation response` [http://identifiers.org/biomodels.teddy/TEDDY_0000108] shown by a system with a single attractor [http://identifiers.org/biomodels.teddy/TEDDY_0000094]. For all initial states sufficiently near to the attractor the system tend to this attractor.
http://identifiers.org/doi/10.1371/journal.pone.0021782
T. Malashchenko, et al. (2011). `Six types of multistability in a neuronal model based on slow calcium current.'. PloS one 6(7):e21782+.
bistable perturbation response
http://identifiers.org/doi/10.1371/journal.pone.0021782
A `perturbation response` [http://identifiers.org/biomodels.teddy/TEDDY_0000108] shown by a system with two different attractors [http://identifiers.org/biomodels.teddy/TEDDY_0000094]. Depending on the initial state the system tend to the one or the other attractor.
http://identifiers.org/doi/10.1371/journal.pone.0021782
T. Malashchenko, et al. (2011). `Six types of multistability in a neuronal model based on slow calcium current.'. PloS one 6(7):e21782+.
multistable perturbation response
http://identifiers.org/doi/10.1371/journal.pone.0021782
A `perturbation response` [http://identifiers.org/biomodels.teddy/TEDDY_0000108] shown by a system with more than two different attractors [http://identifiers.org/biomodels.teddy/TEDDY_0000094]. Depending on the initial state the system tend to one of the attractors.
http://identifiers.org/doi/10.1371/journal.pone.0021782
T. Malashchenko, et al. (2011). `Six types of multistability in a neuronal model based on slow calcium current.'. PloS one 6(7):e21782+.
quasi-periodic oscillation
http://eom.springer.de/Q/q076630.htm
http://identifiers.org/isbn/0738204536
http://www.scholarpedia.org/article/Quasiperiodic_oscillations
QPO
Quasi-periodic oscillation is an oscillation [http://identifiers.org/biomodels.teddy/TEDDY_0000006] that can be described by a quasiperiodic function, i.e. a function f such that f(t)=F(t,...,t) for some continuous function F(t1,...,tn) of n variables that is periodic with respect to t1,...,tn with periods w1,...,wn, respectively. All the w1,...,wn are required to be strictly positive and their reciprocals p1,...,pn have to be rationally linearly independent.
quasiperiodic oscillation
http://www.scholarpedia.org/article/Quasiperiodic_oscillations
Anatoly M. Samoilenko (2007) Quasiperiodic oscillations. Scholarpedia, 2(5):1783.
http://eom.springer.de/Q/q076630.htm
Encyclopaedia of Mathematics, edited by Michiel Hazewinkel, CWI, Amsterdam.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.276)
stable fixed point ((obsolete))
http://identifiers.org/isbn/0738204536
true
Attractor
Obsolete: a fixed point which is stable.
Sink
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.17)
stable limit cycle
http://identifiers.org/isbn/0738204536
If all the neighbouring paths [http://identifiers.org/biomodels.teddy/TEDDY_0000083] approach the limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] then it is stable.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196)
neutrally stable fixed point
http://identifiers.org/isbn/0738204536
A 'fixed point' [http://identifiers.org/biomodels.teddy/TEDDY_0000086] which is neutrally stable [http://identifiers.org/biomodels.teddy/TEDDY_0000098].
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.129)
magnitude
A size of an object.
high magnitude
A magnitude that is much higher than the expected one.
low magnitude
A magnitude that is much lower than the expected one.
saddle-node homoclinic bifurcation
http://identifiers.org/isbn/0387983821
A global bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000147] in which node [http://identifiers.org/biomodels.teddy/TEDDY_0000087] and a saddle [http://identifiers.org/biomodels.teddy/TEDDY_0000089] collide to a saddle [http://identifiers.org/biomodels.teddy/TEDDY_0000089] at the bifurcation point, connected by a homoclinic saddle connection [http://identifiers.org/biomodels.teddy/TEDDY_0000100]. Above the bifurcation point a limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] appears and the saddle [http://identifiers.org/biomodels.teddy/TEDDY_0000089] vanishes. The period of this cycle tends to infinity as the parameter approaches its bifurcation value.
infinite period bifurcation
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.59ff)
http://identifiers.org/isbn/0738204536 (p.262)
infinite period bifurcation
degenerate Hopf bifurcation
http://identifiers.org/isbn/0738204536
A `Hopf bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000072] in which neigther a limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] is destroyed nor a limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] appears. On the bifurcation the fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] is a `center` [http://identifiers.org/biomodels.teddy/TEDDY_0000088].
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.253)
transcritical bifurcation
1
1
1
1
http://identifiers.org/isbn/0738204536
A `zero-eigenvalue bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000123] in which a stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133] fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] and an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] coalesce and exchange their stability.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.50f)
pitchfork bifurcation
2
2
http://identifiers.org/isbn/0738204536
A `zero-eigenvalue bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000123] in which the fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] is surrounded by two symmetrical fixed points on one side of the bifurcation.
flip bifurcation
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.55)
http://identifiers.org/isbn/0198565623 (p.432)
flip bifurcation
zero-eigenvalue bifurcation
http://identifiers.org/isbn/0738204536
A `local bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000069] in which one of the eigenvalue of the linarisation around the fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] is zero at the bifurcation.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.248)
subcritical pitchfork bifurcation
1
1
2
http://identifiers.org/isbn/0738204536
A `pitchfork bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000122] in which two symmetrical stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133] fixed points [http://identifiers.org/biomodels.teddy/TEDDY_0000086] collide with an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] and dissapear, while the unstable fixed point transforms into a stable one.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.58f)
supercritical pitchfork bifurcation
1
2
1
http://identifiers.org/isbn/0738204536
A `pitchfork bifurcation` [http://identifiers.org/biomodels.teddy/TEDDY_0000122] in which two symmetrical stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133] fixed points [http://identifiers.org/biomodels.teddy/TEDDY_0000086] and an unstable [not TEDDY_0000133] fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] appear from a stable fixed point.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.55f)
stable spiral
http://identifiers.org/isbn/0738204536
A spiral point [http://identifiers.org/biomodels.teddy/TEDDY_0000091] which is stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two negative complex conjugate eigenvalues. The fixed point is surrounded by behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083] spiralling downward the fixed point, corresponding to decaying oscillations.
spiral sink
stable focus
stable spiral point
http://identifiers.org/isbn/0198565623 (p.73)
stable spiral point
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137)
http://identifiers.org/isbn/0198565623 (p.25)
stable focus
unstable spiral
http://identifiers.org/isbn/0738204536
A spiral point [http://identifiers.org/biomodels.teddy/TEDDY_0000091] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two positive complex conjugate eigenvalues. The fixed point is surrounded by behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083] spiralling upward the fixed point, corresponding to growing oscillations.
spiral source
unstable focus
unstable spiral point
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (pp.134,137)
http://identifiers.org/isbn/0198565623 (p.73)
unstable spiral point
http://identifiers.org/isbn/0198565623 (p.25)
unstable focus
unstable limit cycle
http://identifiers.org/isbn/0738204536
If all trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] that start near the limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] (both inside and outside) spiral outward, then the limit cycle is called unstable.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196)
unstable fixed point
http://identifiers.org/isbn/0738204536
A fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] which is not Liapunov stable [not TEDDY_0000113].
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.17)
inflexion point
http://mathworld.wolfram.com/InflectionPoint.html
An inflection point is a point on a curve at which the sign of the curvature (i.e., the concavity) changes. Inflection points may be stationary points, but are not local maxima or local minima.
http://mathworld.wolfram.com/InflectionPoint.html
Weisstein, Eric W. Inflection Point. From MathWorld--A Wolfram Web Resource.
amplitude
http://mathworld.wolfram.com/Amplitude.html
A magnitude of an oscillation.
http://mathworld.wolfram.com/Amplitude.html
Weisstein, Eric W. "Amplitude." From MathWorld--A Wolfram Web Resource.
behaviour diversification
Behaviour diversification describes the way one or several temporal behaviours [http://identifiers.org/biomodels.teddy/TEDDY_0000083] are modified or related upon interaction with information external to the system considered.
Lyapunov stability
http://identifiers.org/isbn/0198565623
A solution x*(t) of the n-dimentional system x ̇=X(x, t) is Liapunov stable, if no matter how small is the permitted deviation, measured by epsilon, there still exists a nonzero tolerance, measured by delta, in the initial conditions when the system is activated, allowing it to run satisfactorily.
Liapunov stability
solution stability
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.286)
http://identifiers.org/isbn/0198565623 (p.286)
solution stability
half-stability
http://identifiers.org/isbn/0738204536
An invariant set is called half-stable if there exist a stable and an unstable manifold with respect to the invariant set.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.26,196)
only local stability
http://identifiers.org/isbn/0738204536
An asymptotically stable [http://identifiers.org/biomodels.teddy/TEDDY_0000097] behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] to which only behaviours starting in a restricted neighbourhood will converge.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.20)
global stability
http://identifiers.org/isbn/0738204536
An asymptotically stable [http://identifiers.org/biomodels.teddy/TEDDY_0000097] behaviour [http://identifiers.org/biomodels.teddy/TEDDY_0000083] to which all other behaviours will converge independent of the initial distance.
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.20)
stable node
http://identifiers.org/isbn/0738204536
A fixed point node [http://identifiers.org/biomodels.teddy/TEDDY_0000087] which is stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two negative eigenvalues.
nodal sink
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
unstable node
http://identifiers.org/isbn/0738204536
A fixed point node [http://identifiers.org/biomodels.teddy/TEDDY_0000087] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two positive eigenvalues.
nodal source
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
stable star
http://identifiers.org/isbn/0738204536
A star [http://identifiers.org/biomodels.teddy/TEDDY_0000090] which is stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two identical negative eigenvalues. All other trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] of the system are straight lines towards the fixed point.
stable proper node
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
unstable star
http://identifiers.org/isbn/0738204536
A star [http://identifiers.org/biomodels.teddy/TEDDY_0000090] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two identical positive eigenvalues. All other trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] of the system are straight lines away the fixed point.
unstable proper node
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
stable degenerate node
http://identifiers.org/isbn/0738204536
A degenerated node [http://identifiers.org/biomodels.teddy/TEDDY_0000093] which is stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133], i.e. for which the Jacobian matrix has two identical negative eigenvalues.
degenerate stable node
stable degenerated node
stable improper node
http://identifiers.org/isbn/0198565623 (p.73)
degenerate stable node
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
unstable degenerate node
http://identifiers.org/isbn/0738204536
A degenerated node [http://identifiers.org/biomodels.teddy/TEDDY_0000093] which is unstable [not TEDDY_0000133], i.e. for which the Jacobian matrix has two identical positive eigenvalues.
degenerate unstable point
unstable degenerated node
unstable improper node
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.137)
http://identifiers.org/isbn/0198565623 (p.73)
degenerate unstable point
non-periodic orbit
http://identifiers.org/isbn/9781402014031
A 'temporal behaviour' [http://identifiers.org/biomodels.teddy/TEDDY_0000083] which never repeats its state.
http://identifiers.org/isbn/9781402014031
Coley AA. (2003) Dynamical systems and cosmology, Kluwer Academic Publishers, Dordrecht. (p.10)
monotonicity characteristic
A characteristic describing the order of the successive states of a curve.
half-stable limit cycle
http://identifiers.org/isbn/0738204536
If trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] on one side of the limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] spiral inward and on the other side spiral outward, it is called semistable.
semi-stable limit cycle
semistable limit cycle
http://identifiers.org/isbn/0738204536
Strogatz SH. (2000) Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Cambridge, MA. (p.196)
http://identifiers.org/isbn/0198565623 (p.114)
semi-stable limit cycle
asymptotic behaviour
A `temporal behaviour` [http://identifiers.org/biomodels.teddy/TEDDY_0000083] which converges to some `limit behaviour` [http://identifiers.org/biomodels.teddy/TEDDY_0000085].
global bifurcation
http://identifiers.org/isbn/0387983821
A bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000053] in which at least two limit cycles [http://identifiers.org/biomodels.teddy/TEDDY_0000051] or fixed points TEDDY_0000086 are involved. It can not be detected within a small neighborhood of a fixed point.
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.59)
stability characteristic
A characteristic describing stability of a 'temporal behaviour' [http://identifiers.org/biomodels.teddy/TEDDY_0000083], i.e. how far from each other solutions with close initial states become as time passes.
Poincaré stability
http://identifiers.org/isbn/0198565623
Poisson stability
The solution x*(t), t >= t0 is Poincaré stable, if all sufficiently small disturbances of the initial value a* lead to half-paths remaining for all later time at a small distance from the half-path H* with initial point a*.
orbitally stable behaviour
http://identifiers.org/isbn/0198565623 (p.278)
orbitally stable behaviour
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.278)
http://identifiers.org/isbn/0821803670
Poisson stability
uniform stability
http://identifiers.org/isbn/0198565623
A Liapunov stable [http://identifiers.org/biomodels.teddy/TEDDY_0000133] solution [http://identifiers.org/biomodels.teddy/TEDDY_0000083] is uniformly stable if its sensitivity to disturbance does not increase indefinitely with time.
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.288)
heteroclinic orbit
2
http://identifiers.org/isbn/0198565623
A heteroclinic orbit is a trajectory [http://identifiers.org/biomodels.teddy/TEDDY_0000083] of a dynamical system that tends to two different invariant sets as time approaches positive and negative infinities.
heteroclinic path
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (pp.114-115)
http://identifiers.org/isbn/0198565623 (pp.114-115)
heteroclinic path
homoclinic orbit
1
http://identifiers.org/isbn/0198565623
A homoclinic orbit is a trajectory [http://identifiers.org/biomodels.teddy/TEDDY_0000083] of a dynamical system that tends to the same invariant set as time approaches positive and negative infinities.
homoclinic path
http://identifiers.org/isbn/0198565623 (pp.114-115)
homoclinic path
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (pp.114-115)
heteroclinic bifurcation
http://identifiers.org/isbn/0387983821
A global bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000147] in which two saddles [http://identifiers.org/biomodels.teddy/TEDDY_0000089] are only connected at the bifurcation point by a heteroclinic saddle connection [http://identifiers.org/biomodels.teddy/TEDDY_0000101]. This saddle connection does not exist below and above the bifurcation.
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.59)
homoclinic bifurcation
http://identifiers.org/isbn/0387983821
A global bifurcation [http://identifiers.org/biomodels.teddy/TEDDY_0000147] in which a homoclinic saddle connection [http://identifiers.org/biomodels.teddy/TEDDY_0000100] only exists at the bifurcation point. There exists a Limit Cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] either below or above the bifurcation.
saddle-loop bifurcation
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.200ff)
http://identifiers.org/isbn/0387983821
http://identifiers.org/isbn/0738204536 (p.263)
saddle-loop bifurcation
hyperbolicity
http://identifiers.org/isbn/0198565623
http://identifiers.org/isbn/0387983821
A fixed point [http://identifiers.org/biomodels.teddy/TEDDY_0000086] is said to be hyperbolic if all eigenvalues of the Jacobian matrix have non-zero real parts. A limit cycle [http://identifiers.org/biomodels.teddy/TEDDY_0000051] is called hyperbolic if the fixed point of the Poincare ́map is hyperbolic.
http://identifiers.org/isbn/0198565623
Jordan DW., Smith P. (1999) Nonlinear ordinary differential equations: an introduction to dynamical systems, Oxford University Press. (p.74)
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.55)
two-node positive feedback loop
http://identifiers.org/isbn/1584886420
2-node positive feedback
2-node positive feedback loop
A network motif in which two transcription factors regulate each other with the regulation signs of the two interactions leading to a positive feedback loop.
two-node positive feedback
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.99)
double-positive feedback loop
http://identifiers.org/isbn/1584886420
A positive feedback loop made of two positive interactions, so that the two transcription factors activate each other.
double-positive feedback
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.99)
double-negative feedback loop
http://identifiers.org/isbn/1584886420
A positive feedback loop made of two negative interactions, so that the two transcription factors repress each other.
double-negative feedback
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.99)
multi-output feed-forward loop
http://identifiers.org/isbn/1584886420
A simple topological generalization of the 'three-node feed-forward loop' [http://identifiers.org/biomodels.teddy/TEDDY_0000037] based on multiplication of the output node.
multi-output FFL
http://identifiers.org/isbn/1584886420
Alon U (2006) An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman and Hall/CRC. (p.83)
toggle switch
http://identifiers.org/pubmed/10659857
A two-node double-negative loop.
http://identifiers.org/pubmed/10659857
Gardner TS, Cantor CR, Collins JJ (2000) Construction of a genetic toggle switch in Escherichia coli, Nature; 403(6767):339-42.
structural stability
http://identifiers.org/isbn/0387983821
A system x ̇=f(x), x ∈ Rn (1), defined in a region D ⊂ Rn is called structurally stable in a region D0 ⊂ D if for any sufficiently C1-close in D system x ̇=g(x), x ∈ Rn (2), there are regions U, V ⊂ D, D0 ⊂ U such that (1) is topologically equivalent in U to (2) in V.
Andronov's structural stability
http://identifiers.org/isbn/0387983821
Kuznetsov YA. (1988) Elements of applied bifurcation theory, Springer, New York. (p.71)
regular attractor
http://identifiers.org/isbn/9810221428
The attractor [http://identifiers.org/biomodels.teddy/TEDDY_0000094] is regular or simple if the phase trajectories [http://identifiers.org/biomodels.teddy/TEDDY_0000083] on the attractor are stable according both to Lyapunov [http://identifiers.org/biomodels.teddy/TEDDY_0000113] and to Poisson [http://identifiers.org/biomodels.teddy/TEDDY_0000149].
simple attractor
http://identifiers.org/isbn/9810221428
V. S. Anishchenko (1995) Dynamical Chaos-Models and Experiments: Appearance Routes and Structure of Chaos in Simple Dynamical Systems (World Scientific Series on Nonlinear Science, Series a, Vol 8). World Scientific Pub Co Inc. (p.10)
blue sky catastrophe
A 'bifurcation of limit cycle' [http://identifiers.org/biomodels.teddy/TEDDY_0000070] in which a limit cycle collides with a non-hyperbolic cycle.
curve quantitative characteristic
A quantitative characteristic of the graph of a function.
excitability
http://identifiers.org/doi/10.1142/S0218127400000840
http://identifiers.org/pubmed/16333295
According to the intuitive definition of excitability, small perturbations near the equilibrium can cause large excursions for the solution before it returns to the equilibrium.
http://identifiers.org/pubmed/16333295
Tyson JJ.: Modeling the cell division cycle: cdc2 and cyclin
interactions. Proc Natl Acad Sci U S A. 1991 Aug 15;88(16):7328-32.
http://identifiers.org/doi/10.1142/S0218127400000840
Eugene M. Izhikevich: Neural Excitability, Spiking and Bursting. Int. J. Bifurcation Chaos, 10, 1171 (2000).
_obsolete
true
1
2
http://identifiers.org/isbn/9810221428 (p.10)
http://identifiers.org/isbn/9810221428 (p.10)
3
http://identifiers.org/isbn/0387983821 (p.196)