Noise and O(1) amplitude effects on heteroclinic cycles

Emily Stone, Hans Armbruster

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

The dynamics of structurally stable heteroclinic cycles connecting fixed points with one-dimensional unstable manifolds under the influence of noise is analyzed. Fokker-Planck equations for the evolution of the probability distribution of trajectories near heteroclinic cycles are solved. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitude of the added noise on the location and shape of the probability distribution is determined. As a consequence, the jumping of solution trajectories in and out of invariant subspaces of the deterministic system can be explained.

Original languageEnglish (US)
Pages (from-to)499-506
Number of pages8
JournalChaos
Volume9
Issue number2
StatePublished - Jun 1999

Fingerprint

Heteroclinic Cycle
Probability distributions
Probability Distribution
Fixed point
Trajectories
trajectories
Trajectory
Fokker Planck equation
Unstable Manifold
cycles
Fokker-Planck equation
Invariant Subspace
Fokker-Planck Equation
eigenvalues
Unstable
Eigenvalue
Influence

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Noise and O(1) amplitude effects on heteroclinic cycles. / Stone, Emily; Armbruster, Hans.

In: Chaos, Vol. 9, No. 2, 06.1999, p. 499-506.

Research output: Contribution to journalArticle

Stone, Emily ; Armbruster, Hans. / Noise and O(1) amplitude effects on heteroclinic cycles. In: Chaos. 1999 ; Vol. 9, No. 2. pp. 499-506.
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