 
Summary: Noisy heteroclinic networks
Dieter Armbruster
Department of Mathematics, Arizona State University, Tempe, Arizona 852871804
Emily Stone
Department of Mathematics and Statistics, Utah State University, Logan, Utah 843223900
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 noiseinduced 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
