Noise and O(1) amplitude effects on heteroclinic cycles

Emily Stone, Dieter Armbruster

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


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
Pages (from-to)499-506
Number of pages8
Issue number2
StatePublished - Jun 1999


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