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Noisy heteroclinic networks Dieter Armbruster

Summary: Noisy heteroclinic networks
Dieter Armbruster
Department of Mathematics, Arizona State University, Tempe, Arizona 85287-1804
Emily Stone
Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322-3900
Vivien Kirk
Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Received 15 July 2002; accepted 30 November 2002; published 17 January 2003
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. 2003
American Institute of Physics. DOI: 10.1063/1.1539951
An asymptotically stable heteroclinic cycle is an attractor
of a system of nonlinear differential equations that con-
sists of a finite number of equilibria which are cyclically
connected. Such heteroclinic cycles can occur in a struc-
turally stable way in systems with symmetry and in evo-


Source: Armbruster, Dieter - Department of Mathematics and Statistics, Arizona State University


Collections: Mathematics