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Limit cycle

In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have…

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Applications

Hodgkin–Huxley modelAction potentialsNeuronsGlycolysisCircadian rhythm
10 related topics

Definition

OrbitImageLimit set
3 related topics

Stable, unstable and semi-stable limit cycles

StableAttractorsOscillations
3 related topics

Finding limit cycles

Stationary pointBendixson–Dulac theoremPoincaré–Bendixson theorem
3 related topics

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Overview

Definition

Properties

Stable, unstable and semi-stable limit cycles

Finding limit cycles

Open problems

Applications

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Map overview Semantic statistics

Limit cycle

Nodes35
Edges34
Triples69
Avg. degree1.94
Density0.057143
Components1

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Limit cycle

Top relations

related to Further reading · 35
Limit cycle → Applied Mathematics, Arthur Mattuck, Avalon, Biology, Chaos, Chemistry, Differential Equations, Dover, Dynamical Systems, Engineering, Existence, Geometric Theory, Industrial, ISBN, Lawrence Perko, Lectures, Limit Cycles, MIT Open Courseware, Non-existence Criteria, Nonlinear Dynamics
has application · 10
Limit cycle → Aerodynamic, Hodgkin, Huxley, Limit, Mackey-Glass, Pol, Some, The, The Sel'kov, Van
related to Finding limit cycles · 5
Limit cycle → Bendixson, Dulac, Every, Poincaré, The Bendixson
related to Stable, unstable and semi-stable limit cycles · 5
Limit cycle → If, In, Stable, There, They
related to Open problems · 4
Limit cycle → Finding, Hilbert's, It, The
related to Properties · 4
Limit cycle → By, Given, Jordan, The
related to Definition · 3
Limit cycle → An, Such, We
is a · 2
Limit cycle → closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity, cycle which is the limit set of some other trajectory
related to External links · 1
Limit cycle → Retrieved

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Important terminology

limit trajectory cycle cycles systems displaystyle oscillations closed time approaches stable differential system dynamical infinity nonlinear model behavior mathbb point

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Limit cycleis aclosed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity0.90text
Limit cycleis acycle which is the limit set of some other trajectory0.90text
Limit cyclehas applicationLimit0.60section
Limit cyclehas applicationSome0.60section
Limit cyclehas applicationAerodynamic0.60section
Limit cyclehas applicationHodgkin0.60section
Limit cyclehas applicationHuxley0.60section
Limit cyclehas applicationThe Sel'kov0.60section
Limit cyclehas applicationThe0.60section
Limit cyclehas applicationVan0.60section
Limit cyclehas applicationPol0.60section
Limit cyclehas applicationMackey-Glass0.60section

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