http://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/tags/rel-2007-09-03/ontology/teddy.owl
http://teddyontology.sourceforge.net/
en
rel-2009-10-16 (inferred)
SVN: $HeadURL: https://teddyontology.svn.sourceforge.net/svnroot/teddyontology/teddy/trunk/ontology/teddy.owl $
$Revision: 185 $ $Date: 2009-10-16 09:09:12 +0200 (Fr, 16. Okt 2009) $
$Author: tral $
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.
classified by Pellet 0.9.3 with Protege 4.0.113
TErminology for the Description of DYnamics (TEDDY)
An Asymptotic Behaviour is a Temporal Behaviour to which behaviours starting nearby tend as time goes to either positive or negative infinity.
Asymptotic State
Limit Set
Asymptotic Behaviour
urn:miriam:isbn:0387983821 (p.10)
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Curve ((obsolete))
Limit
Repelling
urn:miriam:isbn:0738204536 (p.129)
A Behaviour is Unstable if it is neither Liapunov Stable nor Attracting.
Unstable
Neimark-Sacker Bifurcation of Limit-Cycles
NSLC
synonym "NSLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
Non-Isolated Cycle
urn:miriam:isbn:0738204536 (p.196)
A Non-Isolated Cycle is a Cycle which is surrounded by other Cycles.
Neutrally Stable Cycle
Infinite-Period 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
Saddle-Node Homoclinic Bifurcation
A Liapunov Stable Fixed Point is a Fixed Point which is Liapunov Stable.
urn:miriam:isbn:0738204536 (p.129)
Liapunov Stable Fixed Point
C4-FFL
Coherent 3-node Feedforward Type-4
Obsolete: not required anymore.
Regularity ((obsolete))
Low Magnitude
Exponential Growth
Period-Doubling Bifurcation of Limit-Cycles
synonym "PDLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
PDLC
A Behaviour is Stable if it is Liapunov Stable and Attracting.
urn:miriam:isbn:0738204536 (p.129)
Asymptotically Stable
Stable
Obsolete: not required anymore.
Parametrical Behaviour ((obsolete))
Infinite Limit
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Temporal Behaviour ((obsolete))
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
Integrator
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
Oscillating
Plus Infinity Limit
Linear Decreasing
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.
urn:miriam:isbn:0738204536 (p.26)
Half-Stable Fixed Point
A Saddle Point is a Fixed Point for which the Jacobian matrix has real-valued eigenvalues of opposite signs.
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).
urn:miriam:isbn:0738204536 (p.196)
Unstable Limit Cycle
An Unstable Limit Cycle is a Limit Cycle which is Unstable.
Curve Characteristic
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.
Strictly Increasing (Isotonic)
A curve is Strictly Increasing if it is Strictly Monotonic with temporal successive states increasing ordered.
1
Magnitude
Incoherent 3-node Feedforward Type-3
I3-FFL
Obsolete: not required anymore.
Parameter Dependency ((obsolete))
Asymptotic Increasing
Minus Infinity Limit
Perturbation Behaviour
A ``Perturbation Behaviour'' is a ``Behaviour'' with respect to perturbations of the system or its environment.
urn:miriam:isbn:0738204536 (p.129)
A Neutrally Stable Fixed Point is a Fixed Point which is Neutrally Stable.
Neutrally Stable Fixed Point
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
urn:miriam:isbn:0738204536 (p.196)
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.
Half-Stable Limit Cycle
Non-Periodically Oscillating
Coherent 3-node Feedforward Type-3
C3-FFL
Stable Limit Cycle
A Stable Limit Cycle is a Limit Cycle which is Stable.
urn:miriam:isbn:0738204536 (p.196)
Concave Shape
Sustained Oscillation ((obsolete))
Obsolete: equivalent to TEDDY_0000051 "Limit Cycle".
Non-Periodic Orbit
urn:miriam:isbn:9781402014031 (p.10)
A Non-Periodic Orbit is a Temporal Behaviour which never repeats a state.
Improper Node
Degenerated Node
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.
urn:miriam:isbn:0738204536 (p.135f)
urn:miriam:isbn:3817112823 (p.53)
Stability is a Behaviour Characteristic describing behaviours starting near the characterised behaviour. The "nearness" between behaviours requires an appropriate metric.
Stability
Sink
Stable Fixed Point
urn:miriam:isbn:0738204536 (p.17)
A Stable Fixed Point is a Fixed Point which is Stable.
Attractor
Diverging Increasing
Stable Spiral Point
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.
urn:miriam:isbn:0738204536 (p.134,137)
A curve is Strictly Monotonic if it is Monotonic and has no equal temporal successive states.
Strictly Monotonic
_obsolete
Asymptotic Decreasing
Grenzzyklus
urn:miriam:isbn:0738204536 (p.196)
Limit Cycle
German synonym Grenzzyklus: ISBN 3817112823
A Limit Cycle is a Closed Orbit which is isolated, i.e. neighbouring Orbits are not closed.
urn:miriam:isbn:0738204536 (p.137)
Stable Node
A Stable Node is a Fixed Point Node which is Stable, i.e. for which the Jacobian Matrix has two negative eigenvalues.
urn:miriam:isbn:0738204536 (p.128)
A Behaviour is Attracting if all behaviours starting sufficiently near to the set will approach it.
Attracting
urn:miriam:isbn:0738204536 (p.129)
Neutrally Stable
A Behaviour is Neutrally Stable if it is Liapunov Stable and not Attracting.
Transcritical Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.50f
A ``Transcritical Bifurcation'' is a ``Zero-Eigenvalue Bifurcation'' in which a ``Stable Fixed Point'' and an ``Unstable Fixed Point'' coalesce and exchange their stability.
Asymptotic Upper Limit
Straight Line Shape
_obsolete Behaviour ((obsolete))
Obsolete: only one obsolete branch required.
Feedback
Stable Behaviour
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.
I2-FFL
Incoherent 3-node Feedforward Type-2
Curve Shape
Unstable Behaviour
Repeller
A ``Repeller'' is a ``repelling'' ``Asymptotic Behaviour''.
Fold Bifurcation
Tangent Bifurcation
Limit Point Bifurcation
Turning-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
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
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.
Unstable Degenerated Node
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.
urn:miriam:isbn:0738204536 (p.137)
Convex Shape
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.
Stable Star
urn:miriam:isbn:0738204536 (p.137)
Non-Monotonic
A curve is Non-Monotonic if it has both increasing ordered successive states and decreasing orderd succesive states.
Zero Growth
Coherent 3-node Feedforward
Periodically Oscillating
urn:miriam:isbn:0738204536 (p.20)
A Behaviour is Only Locally Stable if it is Stable, but only behaviours starting in a restricted neighbourhood will approach it.
Only Locally Stable
Linear Growth
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 Andronov-Hopf Bifurcation (Subc-AH)
synonym "Subcritical Andronov-Hopf Bifurcation (Subc-AH)": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
Subcritical Hopf Bifurcation
Obsolete: only one obsolete branch required.
_obsolete Functionality ((obsolete))
Asymptotic Lower Limit
Period
Behaviour Characteristic
SNLC
synonym "SNLC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
Saddle-Node Bifurcation of Limit-Cycles
High Magnitude
Saddle-Node on Invariant Circle Bifurcation
synonym "SNIC": http://www.tbi.univie.ac.at/wiki/index.php/Classification_of_Dynamical_Behaviors
SNIC
urn:miriam:isbn:0738204536 (p.134,137)
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.
Center
Elliptic Fixed Point
Incoherent 3-node Feedforward
Inflexion Point
An Unstable Fixed Point is a Fixed Point which is Unstable.
Source
Repeller
urn:miriam:isbn:0738204536 (p.17)
Unstable Fixed Point
A Heteroclinic Orbit is a Saddle Connection connecting two different Saddle Points.
Heteroclinic Orbit
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)).
Synonyms: Heteroclinic Trajectory (urn:miriam:isbn:0738204536 p.166)
Heteroclinic Trajectory
urn:miriam:isbn:0738204536 (p.166)
A Homoclinic Orbit is a Saddle Connection connecting a Saddle Point to itself.
Homoclinic Loop
Saddle Loop
Synonyms: Homoclinic Loop (urn:miriam:isbn:3540971416 p.213), Saddle Loop (http://www.egwald.ca/nonlineardynamics/mathappendix.php#limitset)
urn:miriam:isbn:0738204536 (p.161)
Homoclinic Orbit
Amplitude
Obsolete: equivalent to TEDDY_0000083 "Temporal Behaviour".
Orbit ((obsolete))
Quasiperiodic Oscillating
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.276
http://www.scholarpedia.org/article/Quasiperiodic_oscillations
urn:miriam:isbn:0738204536 (p.134,137)
Unstable Spiral Point
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.
Obsolete: equivalent to TEDDY_0000086 "Fixed Point".
Steady State ((obsolete))
3
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
Unbounded 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.
A curve is Strictly Decreasing if it is Strictly Monotonic with temporal successive states decreasing ordered.
Strictly Decreasing (Antitonic)
urn:miriam:isbn:0738204536 (p.184)
A Saddle Connection is a Temporal Behaviour connecting two Saddle Points.
Saddle Connection
urn:miriam:isbn:0738204536 (p.137)
Unstable Node
An Unstable Node is a Fixed Point Node which is Unstable, i.e. for which the Jacobian Matrix has two positive eigenvalues.
Bistable Behaviour
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.
2
Incoherent 3-node Feedforward Type-4
I4-FFL
Damped Oscillating
Monotonic
http://mathworld.wolfram.com/MonotonicFunction.html
A curve is ``Monotonic'' if successive states are orderd either entirely non-decreasing or entirely non-increasing.
Spiral Point
urn:miriam:isbn:0738204536 (p.134,137)
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.
Positive Feedback
Switch
urn:miriam:isbn:0738204536 (p.26,196)
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.
Half-Stable
Fixed Point ((obsolete))
Obsolete: equivalent to TEDDY_0000086 "Fixed Point".
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.
Star
urn:miriam:isbn:0738204536 (p.135)
Single Turnaround
Bursting
3-node Feedforward
A ``Subcritical Pitchfork Bifurcation'' is a ``Pitchfork Bifurcation'' in which two symmetrical ``Unstable Fixed Points'' collide with the stable fixed point and disappear.
Subcritical Pitchfork Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.58f
Polynomial Growth
Incoherent 3-node Feedforward Type-1
I1-FFL
An '''Attractor''' is an ''Asymptotic Behaviour'' to which all neighboring trajectories converge.
Attractor
ISBN 0738204536 (p.324)
Sigmoid Shape
Non-isolated Fixed Point
urn:miriam:isbn:0738204536 (p.128,137)
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.
Negative Feedback
Coherent 3-node Feedforward Type-1
C1-FFL
Bifurcation from Limit Cycle
Fixed Point Node
urn:miriam:isbn:0738204536 (p.137)
A Fixed Point Node is a Fixed Point for which the Jacobian matrix has real-valued eigenvalues of the same sign.
Mixed-Mode Oscillating
Behaviour Diversification
Monotonicity
Asymptotic Limit
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
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
urn:miriam:isbn:0738204536 (p.137)
Stable Improper Node
_obsolete Characteristic ((obsolete))
Obsolete: only one obsolete branch required.
A ``Supercritical Hopf Bifurcation'' is a ``Hopf Bifurcation'' in which an ``Stable Limit Cycle'' appears.
Supercritical Andronov-Hopf Bifurcation (Supc-AH)
Supercritical Hopf Bifurcation
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
synonym "Andronov-Hopf Bifurcation": http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#kuznetsov98-bifurcation_theory, p.80
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.
Hopf Bifurcation
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.248ff
Andronov-Hopf Bifurcation
A Strange Attractor is an Non-Periodic Orbit which is Attracting and exhibits sensitive dependence on initial conditions.
Fractal Attractor
Strange Attractor
Chaotic Attractor
Synonyms "Chaotic Attractor", "Fractal Attractor": urn:miriam:isbn:0738204536 (p.325)
urn:miriam:isbn:0738204536 (p.325)
Growth
1
1
A ``Bifurcation'' is a ``Characteristic'' describing a qualitative (topological) change in the orbit structure of a system.
Bifurcation
http://www.egwald.com/nonlineardynamics/bifurcations.php
C2-FFL
Coherent 3-node Feedforward Type-2
A Periodic Orbit is a Temporal Behaviour which repeats every state after a specific period of time.
Periodic Orbit
urn:miriam:isbn:0387983821 (p.9)
Periodic Solution
Closed Orbit
Cycle
Linear Increasing
Single-Periodically Oscillating
http://www.ebi.ac.uk/compneur-srv/teddy/literature.html#strogatz01-nonlinear_dynamics, p.55
Pitchfork Bifurcation
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.
Functional Motif
urn:miriam:isbn:0738204536 (p.129)
Liapunov Stable
A Behaviour is Liapunov Stable if all behaviours starting sufficiently near to the set remain close to it.
Feedforward
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.
Unstable Star
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.
A Neutrally Stable Behaviour is a Temporal Behaviour which is neither Attracting nor Unstable.
Neutrally Stable Behaviour
urn:miriam:isbn:0738204536 (p.129)
Non-Isolated Asymptotic Behaviour
This relation is used to describe properties of a Temporal Behaviour by means of Behaviour Characteristic.
hasCharacteristic
hasOnPart
partOf
hasSuperPart
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.
hasStability
This relation describes the Stability of a Temporal Behaviour.
adjacentTo
Two Temporal Behaviours are adjacentTo each other if and only if they are in phase space proximity.
hasPart
hasSubPart
hasValue