Noisy heteroclinic networks

Hans Armbruster; Emily Stone; Vivien Kirk

doi:10.1063/1.1539951

Noisy heteroclinic networks

Hans Armbruster, Emily Stone, Vivien Kirk

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

The influence of small noise on the dynamics of heteroclinic networks is studied, with a particular focus on noise-induced switching between cycles in the network. Three different types of switching are found, depending on the details of the underlying deterministic dynamics: random switching between the heteroclinic cycles determined by the linear dynamics near one of the saddle points, noise induced stability of a cycle, and intermittent switching between cycles. All three responses are explained by examining the size of the stable and unstable eigenvalues at the equilibria.

Original language	English (US)
Pages (from-to)	71-79
Number of pages	9
Journal	Chaos
Volume	13
Issue number	1
DOIs	https://doi.org/10.1063/1.1539951
State	Published - Mar 2003

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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title = "Noisy heteroclinic networks",

abstract = "The influence of small noise on the dynamics of heteroclinic networks is studied, with a particular focus on noise-induced switching between cycles in the network. Three different types of switching are found, depending on the details of the underlying deterministic dynamics: random switching between the heteroclinic cycles determined by the linear dynamics near one of the saddle points, noise induced stability of a cycle, and intermittent switching between cycles. All three responses are explained by examining the size of the stable and unstable eigenvalues at the equilibria.",

author = "Hans Armbruster and Emily Stone and Vivien Kirk",

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AB - The influence of small noise on the dynamics of heteroclinic networks is studied, with a particular focus on noise-induced switching between cycles in the network. Three different types of switching are found, depending on the details of the underlying deterministic dynamics: random switching between the heteroclinic cycles determined by the linear dynamics near one of the saddle points, noise induced stability of a cycle, and intermittent switching between cycles. All three responses are explained by examining the size of the stable and unstable eigenvalues at the equilibria.

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Noisy heteroclinic networks

Abstract

ASJC Scopus subject areas

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