en
http://teddyontology.sourceforge.net/
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.
TErminology for the Description of DYnamics (TEDDY)
http://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/tags/rel-2007-09-03/ontology/teddy.owl
rel-2009-10-16
SVN: $HeadURL: https://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/trunk/ontology/teddy.owl $
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$Author: tral $
Pitchfork Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.55
A ``Pitchfork Bifurcation'' is a ``Zero-Eigenvalue Bifurcation'' in which the fixed point is surrounded by two symmetrical fixed points on one side of the bifurcation.
A ``Transcritical Bifurcation'' is a ``Zero-Eigenvalue Bifurcation'' in which a ``Stable Fixed Point'' and an ``Unstable Fixed Point'' coalesce and exchange their stability.
Transcritical Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.50f
Functional Motif
Convex Shape
Parametrical Behaviour ((obsolete))
Obsolete: not required anymore.
Polynomial Growth
urn:miriam:isbn:0738204536 (p.20)
Globally Stable
A Behaviour is Globally Stable if it is Stable and all other behaviours will approach it.
Positive Feedback
An '''Attractor''' is an ''Asymptotic Behaviour'' to which all neighboring trajectories converge.
ISBN 0738204536 (p.324)
Attractor
Coherent 3-node Feedforward
A ``Supercritical Hopf Bifurcation'' is a ``Hopf Bifurcation'' in which an ``Stable Limit Cycle'' appears.
Supercritical Andronov-Hopf Bifurcation (Supc-AH)
synonym "Supercritical Andronov-Hopf Bifurcation (Supc-AH)": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.249
Supercritical Hopf Bifurcation
1
Magnitude
Bursting
Coherent 3-node Feedforward Type-3
C3-FFL
A Stable Degenerated Node is a Degenerated Node which is Stable, i.e. for which the Jacobian Matrix has two identical negative eigenvalues.
Stable Degenerated Node
Stable Improper Node
urn:miriam:isbn:0738204536 (p.137)
Single-Periodically Oscillating
Repeller
Unstable Behaviour
A ``Repeller'' is a ``repelling'' ``Asymptotic Behaviour''.
Monotonic
A curve is ``Monotonic'' if successive states are orderd either entirely non-decreasing or entirely non-increasing.
http://mathworld.wolfram.com/MonotonicFunction.html
A ``Degenerate Hopf Bifurcation'' is a ``Hopf Bifurcation'' in which neigther a Limit Cycle is destroyed nor a Limit Cycle appears. On the bifurcation the fixed point is a ``Center''.
Degenerate Hopf Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.253
Zero-Eigenvalue Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.248
A ``Zero-Eigenvalue Bifurcation'' is a ``Local Bifurcation'' in which one of the eigenvalue of the linarisation around the fixed point is zero at the bifurcation.
Phase Curve
urn:miriam:isbn:0387983821 (p.8)
Solution Curve
Synonyms: Orbit (urn:miriam:isbn:0387983821 p.8), Trajectory (urn:miriam:isbn:0387983821 p.8), Solution Curve (urn:miriam:isbn:0387908196 p.2)
Trajectory
Orbit
A Temporal Behaviour is a temporal sequence of states following the evolution operator of the dynamical system through a given initial state.
Temporal Behaviour
Straight Line Shape
A Stable Node is a Fixed Point Node which is Stable, i.e. for which the Jacobian Matrix has two negative eigenvalues.
Stable Node
urn:miriam:isbn:0738204536 (p.137)
High Magnitude
Improper Node
Degenerated Node
urn:miriam:isbn:0738204536 (p.135f)
A Degenerated Node is a Fixed Point for which the Jacobian Matrix has identical eigenvalues and only one independent eigenvector. All other trajectories of the system asymptotically become parallel to the unique eigendirection.
3-node Feedforward
Feedforward
Switch
Subcritical Andronov-Hopf Bifurcation (Subc-AH)
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.88
A ``Subcritical Hopf Bifurcation'' is a ``Hopf Bifurcation'' in which an ``Unstable Limit Cycle'' is destroyed.
Subcritical Hopf Bifurcation
synonym "Subcritical Andronov-Hopf Bifurcation (Subc-AH)": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
C4-FFL
Coherent 3-node Feedforward Type-4
Zero Growth
Unstable Star
urn:miriam:isbn:0738204536 (p.137)
An Unstable Star is a Star which is Unstable, i.e. for which the Jacobian Matrix has two identical positive eigenvalues. All other trajectories of the system are straight lines away the Fixed Point.
A Behaviour is Attracting if all behaviours starting sufficiently near to the set will approach it.
urn:miriam:isbn:0738204536 (p.128)
Attracting
Damped Oscillating
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Curve ((obsolete))
Subcritical Pitchfork Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.58f
A ``Subcritical Pitchfork Bifurcation'' is a ``Pitchfork Bifurcation'' in which two symmetrical ``Unstable Fixed Points'' collide with the stable fixed point and disappear.
Curve Characteristic
_obsolete Functionality ((obsolete))
Obsolete: only one obsolete branch required.
An one-dimensional Fixed Point is Half-Stable if it is Attracting in one direction and Unstable in the other direction. A two-dimensional Limit Cycle is Half-Stable if it is Attracting outside and Unstable inside or vice versa.
urn:miriam:isbn:0738204536 (p.26,196)
Half-Stable
Strictly Decreasing (Antitonic)
A curve is Strictly Decreasing if it is Strictly Monotonic with temporal successive states decreasing ordered.
Feedback
Unstable
Repelling
A Behaviour is Unstable if it is neither Liapunov Stable nor Attracting.
urn:miriam:isbn:0738204536 (p.129)
Stable Limit Cycle
A Stable Limit Cycle is a Limit Cycle which is Stable.
urn:miriam:isbn:0738204536 (p.196)
Half-Stable Fixed Point
urn:miriam:isbn:0738204536 (p.26)
A Half-Stable Fixed Point is an one-dimensional Fixed Point which is Half-Stable, i.e. the Fixed Point is Attracting in one direction and Unstable in the other direction.
Incoherent 3-node Feedforward
SNLC
synonym "SNLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
Saddle-Node Bifurcation of Limit-Cycles
Obsolete: equivalent to TEDDY_0000051 "Limit Cycle".
Sustained Oscillation ((obsolete))
A ``Bifurcation'' is a ``Characteristic'' describing a qualitative (topological) change in the orbit structure of a system.
http://www.egwald.com/nonlineardynamics/bifurcations.php
1
1
Bifurcation
Unbounded Growth
Supercritical Pitchfork Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.55f
A ``Supercritical Pitchfork Bifurcation'' is a ``Pitchfork Bifurcation'' in which two symmetrical ``Stable Fixed Points'' appear from the stable fixed point.
Behaviour Characteristic
Plus Infinity Limit
Bifurcation of Equilibrium
synonym "Bifurcation from Steady State (EP)": http://www.scholarpedia.org/article/MATCONT
synonyms "Bifurcation of Equilibrium", "Bifurcation of Fixed Point": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.58
http://en.wikipedia.org/wiki/Bifurcation_theory#Local_bifurcations
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.58
A ``Local Bifurcation'' is a ``Bifurcation'' in which a ``Stable Fixed Point'' changes to an unstable 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 (EP)
Local Bifurcation
Bifurcation of Fixed Point
Obsolete: equivalent to TEDDY_0000086 "Fixed Point".
Fixed Point ((obsolete))
Obsolete: only one obsolete branch required.
_obsolete Characteristic ((obsolete))
Coherent 3-node Feedforward Type-1
C1-FFL
urn:miriam:isbn:0738204536 (p.129)
A Liapunov Stable Fixed Point is a Fixed Point which is Liapunov Stable.
Liapunov Stable Fixed Point
Negative Feedback
A Behaviour is Only Locally Stable if it is Stable, but only behaviours starting in a restricted neighbourhood will approach it.
urn:miriam:isbn:0738204536 (p.20)
Only Locally Stable
Linear Increasing
A Strange Attractor is an Non-Periodic Orbit which is Attracting and exhibits sensitive dependence on initial conditions.
Fractal Attractor
Chaotic Attractor
Synonyms "Chaotic Attractor", "Fractal Attractor": urn:miriam:isbn:0738204536 (p.325)
Strange Attractor
urn:miriam:isbn:0738204536 (p.325)
A Neutrally Stable Fixed Point is a Fixed Point which is Neutrally Stable.
urn:miriam:isbn:0738204536 (p.129)
Neutrally Stable Fixed Point
Saddle-Node on Invariant Circle Bifurcation
synonym "SNIC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
SNIC
Non-Periodically Oscillating
Incoherent 3-node Feedforward Type-1
I1-FFL
Neutrally Stable Behaviour
Non-Isolated Asymptotic Behaviour
A Neutrally Stable Behaviour is a Temporal Behaviour which is neither Attracting nor Unstable.
urn:miriam:isbn:0738204536 (p.129)
Saddle Point
urn:miriam:isbn:0738204536 (p.137)
Is also called ''Hyperbolic Fixed Point'' (http://mathworld.wolfram.com/HyperbolicFixedPoint.html), but ''Hyperbolic Fixed Point'' is also used for ''Non-Elliptic Fixed Point'', i.e. eigenvalues are not purely imaginary (References#strogatz00, p.155; http://www.egwald.ca/nonlineardynamics/twodimensionaldynamics.php#topologicalclassification).
A Saddle Point is a Fixed Point for which the Jacobian matrix has real-valued eigenvalues of opposite signs.
Elliptic Fixed Point
Center
A Center is a Fixed Point 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.
urn:miriam:isbn:0738204536 (p.134,137)
Grenzzyklus
Limit Cycle
A Limit Cycle is a Closed Orbit which is isolated, i.e. neighbouring Orbits are not closed.
German synonym Grenzzyklus: ISBN 3817112823
urn:miriam:isbn:0738204536 (p.196)
NSLC
Neimark-Sacker Bifurcation of Limit-Cycles
synonym "NSLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
Regularity ((obsolete))
Obsolete: not required anymore.
A Stable Spiral Point is a Spiral Point which is Stable, i.e. for which the Jacobian Matrix has two negative complex conjugate eigenvalues. The Fixed Point is surrounded by behaviours spiralling downward the Fixed Point, corresponding to decaying oscillations.
Stable Spiral Point
urn:miriam:isbn:0738204536 (p.134,137)
Neutrally Stable
A Behaviour is Neutrally Stable if it is Liapunov Stable and not Attracting.
urn:miriam:isbn:0738204536 (p.129)
Minus Infinity Limit
Diverging Increasing
A Half-Stable Limit Cycle is a Limit Cycle which is Half-Stable, i.e. the Limit Cycle is Attracting outside and Unstable inside or vice versa.
urn:miriam:isbn:0738204536 (p.196)
Half-Stable Limit Cycle
Asymptotic Lower Limit
Incoherent 3-node Feedforward Type-2
I2-FFL
A curve is Strictly Monotonic if it is Monotonic and has no equal temporal successive states.
Strictly Monotonic
urn:miriam:isbn:0738204536 (p.196)
A Non-Isolated Cycle is a Cycle which is surrounded by other Cycles.
Neutrally Stable Cycle
Non-Isolated Cycle
Growth
Asymptotic Increasing
Exponential Growth
http://www.scholarpedia.org/article/Quasiperiodic_oscillations
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.276
Quasiperiodic Oscillating
Bifurcation from Limit Cycle
Amplitude
A Fixed Point Node is a Fixed Point for which the Jacobian matrix has real-valued eigenvalues of the same sign.
urn:miriam:isbn:0738204536 (p.137)
Fixed Point Node
Sigmoid Shape
Stable
urn:miriam:isbn:0738204536 (p.129)
Asymptotically Stable
A Behaviour is Stable if it is Liapunov Stable and Attracting.
PDLC
Period-Doubling Bifurcation of Limit-Cycles
synonym "PDLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
Parameter Dependency ((obsolete))
Obsolete: not required anymore.
Period
An Unstable Spiral Point is a Spiral Point which is Unstable, i.e. for which the Jacobian Matrix has two positive complex conjugate eigenvalues. The Fixed Point is surrounded by behaviours spiralling upward the Fixed Point, corresponding to growing oscillations.
Unstable Spiral Point
urn:miriam:isbn:0738204536 (p.134,137)
Asymptotic Upper Limit
Star
A Star is a Fixed Point for which the Jacobian Matrix has identical eigenvalues and two independent corresponding eigenvectors. All other trajectories of the system lie on straight through the Fixed Point.
urn:miriam:isbn:0738204536 (p.135)
Monotonicity
Inflexion Point
Strictly Increasing (Isotonic)
A curve is Strictly Increasing if it is Strictly Monotonic with temporal successive states increasing ordered.
Incoherent 3-node Feedforward Type-3
I3-FFL
Steady State ((obsolete))
Obsolete: equivalent to TEDDY_0000086 "Fixed Point".
Linear Growth
A Stable Fixed Point is a Fixed Point which is Stable.
Stable Fixed Point
urn:miriam:isbn:0738204536 (p.17)
Sink
Attractor
Temporal Behaviour ((obsolete))
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Obsolete: only one obsolete branch required.
_obsolete Behaviour ((obsolete))
Unstable Node
urn:miriam:isbn:0738204536 (p.137)
An Unstable Node is a Fixed Point Node which is Unstable, i.e. for which the Jacobian Matrix has two positive eigenvalues.
Equilibrium
Steady State
Constant Solution
Critical Point
Fixed Point
Constant Behaviour
Rest Solution
http://mathworld.wolfram.com/FixedPoint.html
A Fixed Point is a Temporal Behaviour which does not change its state.
Equilibrium Point
Non-Monotonic
A curve is Non-Monotonic if it has both increasing ordered successive states and decreasing orderd succesive states.
Periodically Oscillating
_obsolete
Low Magnitude
TEDDY Entity
A TEDDY Entity is 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.
I4-FFL
Incoherent 3-node Feedforward Type-4
Asymptotic Limit
Synonyms: Homoclinic Loop (urn:miriam:isbn:3540971416 p.213), Saddle Loop (http://www.egwald.ca/nonlineardynamics/mathappendix.php#limitset)
Homoclinic Orbit
urn:miriam:isbn:0738204536 (p.161)
A Homoclinic Orbit is a Saddle Connection connecting a Saddle Point to itself.
Saddle Loop
Homoclinic Loop
urn:miriam:isbn:9781402014031 (p.10)
A Non-Periodic Orbit is a Temporal Behaviour which never repeats a state.
Non-Periodic Orbit
urn:miriam:isbn:0738204536 (p.196)
An Unstable Limit Cycle is a Limit Cycle which is Unstable.
Unstable Limit Cycle
Spiral Point
A Spiral Point is a Fixed Point for which the Jacobian matrix has not purely imaginary complex conjugate eigenvalues. The Fixed Point is surrounded by spiralling behaviours.
urn:miriam:isbn:0738204536 (p.134,137)
A Behaviour is Liapunov Stable if all behaviours starting sufficiently near to the set remain close to it.
Liapunov Stable
urn:miriam:isbn:0738204536 (p.129)
Bistable Behaviour
2
A ``Bistable Behaviour'' is a ``Perturbation Behaviour'' shown by a system with two different ``Attractor''s. Depending on the initial state the system tend to the one or the other attractor.
Concave Shape
Perturbation Behaviour
A ``Perturbation Behaviour'' is a ``Behaviour'' with respect to perturbations of the system or its environment.
urn:miriam:isbn:3817112823 (p.53)
Stability
Stability is a Behaviour Characteristic describing behaviours starting near the characterised behaviour. The "nearness" between behaviours requires an appropriate metric.
Single Turnaround
Andronov-Hopf Bifurcation
A ``Hopf Bifurcation'' is a ``Local Bifurcation'' in which a ``Stable Spiral'' changes in an ``Unstable Spiral''. The linearisation around the fixed point has two conjugate eigenvalues. This eigenvalues cross simultaneously the imaginary axis from left (negative real part) to the right during the bifurcation.
synonym "Andronov-Hopf Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.80
Hopf Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.248ff
Integrator
Cycle
Closed Orbit
Periodic Solution
urn:miriam:isbn:0387983821 (p.9)
A Periodic Orbit is a Temporal Behaviour which repeats every state after a specific period of time.
Periodic Orbit
Linear Decreasing
Infinite Limit
A Saddle Connection is a Temporal Behaviour connecting two Saddle Points.
urn:miriam:isbn:0738204536 (p.184)
Saddle Connection
Asymptotic Behaviour
Limit Set
Asymptotic State
An Asymptotic Behaviour is a Temporal Behaviour to which behaviours starting nearby tend as time goes to either positive or negative infinity.
urn:miriam:isbn:0387983821 (p.10)
Coherent 3-node Feedforward Type-2
C2-FFL
Oscillating
Mixed-Mode Oscillating
Infinite-Period Bifurcation
Saddle-Node Homoclinic Bifurcation
synonym "Infinite-Period Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.262
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.59ff
Unstable Improper Node
An Unstable Degenerated Node is a Degenerated Node which is Unstable, i.e. for which the Jacobian Matrix has two identical positive eigenvalues.
Unstable Degenerated Node
urn:miriam:isbn:0738204536 (p.137)
urn:miriam:isbn:0738204536 (p.17)
Repeller
Source
Unstable Fixed Point
An Unstable Fixed Point is a Fixed Point which is Unstable.
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Orbit ((obsolete))
Limit
urn:miriam:isbn:0738204536 (p.166)
Heteroclinic Orbit
Heteroclinic Trajectory
A Heteroclinic Orbit is a Saddle Connection connecting two different Saddle Points.
Synonyms: Heteroclinic Trajectory (urn:miriam:isbn:0738204536 p.166)
The term ''Saddle Connection'' is used as a synonym for a heteroclinic orbit (urn:miriam:isbn:0738204536 (p.166) ). But ''Saddle Connection'' is also used for both: homoclinic and heteroclinic orbits (urn:miriam:isbn:0387943773 (p.184)).
A Non-Isolated Fixed Point is a Fixed Point 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.
urn:miriam:isbn:0738204536 (p.128,137)
Non-isolated Fixed Point
Behaviour Diversification
A Stable Star is a Star which is Stable, i.e. for which the Jacobian Matrix has two identical negative eigenvalues. All other trajectories of the system are straight lines towards the Fixed Point.
urn:miriam:isbn:0738204536 (p.137)
Stable Star
Fold Bifurcation
Tangent Bifurcation
Limit Point Bifurcation
synonyms "Fold Bifurctaion", "Turning-Point Bifurcation", "Blue Sky Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.47
Turning-Point Bifurcation
synonym "Tangent Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.80
synonym "Limit Point Bifurcation": http://www.scholarpedia.org/article/Saddle-node_Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.80
A ``Saddle-Node Bifurcation'' is a ``Zero-Eigenvalue Bifurcation'' in which a ``Stable Fixed Point'' and an ``Unstable Fixed Point'' collide and mutually annihilate.
Saddle-Node Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.45
Blue Sky Bifurcation
Asymptotic Decreasing
Curve Shape
A ``Multistable Behaviour'' is a ``Perturbation Behaviour'' shown by a system with more than two different ``Attractor''s. Depending on the initial state the system tend to one of the attractors.
Multistable Behaviour
3
A ``Stable Behaviour'' is a ``Perturbation Behaviour'' shown by a system with a single ``Attractor''. For all initial states sufficiently near to the attractor the system tend to this attractor.
Stable Behaviour
convergeTo
A Temporal Behaviour convergeTo another Temporal Behaviour if and only if it reaches the other Behaviour as time goes to either positive or negative infinity.
hasOnPart
hasSubPart
hasPart
partOf
hasSuperPart
hasValue
Two Temporal Behaviours are adjacentTo each other if and only if they are in phase space proximity.
adjacentTo
This relation describes the Stability of a Temporal Behaviour.
hasStability
This relation is used to describe properties of a Temporal Behaviour by means of Behaviour Characteristic.
hasCharacteristic