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Collections of heteroclinic cycles in the Kuramoto-Sivashinsky equation

Authors
Journal
Physica D Nonlinear Phenomena
0167-2789
Publisher
Elsevier
Publication Date
Volume
100
Identifiers
DOI: 10.1016/s0167-2789(96)00209-6
Keywords
  • Kuramoto-Sivashinsky
  • Attracting Heteroclinic Cycles

Abstract

Abstract We study the Kuramoto-Sivashinky equation with periodic boundary conditions in the case of low-dimensional behavior. We analyze the bifurcations that occur in a six-dimensional (6D) approximation of its inertial manifold. We mainly focus on the attracting and structurally stable heteroclinic connections that arise for these parameter values. We reanalyze the ones that were previously described via a 4D reduction to the center-unstable manifold (Ambruster et al., 1988, 1989). We also find a parameter region for which a manifold of structurally stable heteroclinic cycles exist. The existence of such a manifold is responsible for an intermittent behavior which has some features of unpredictability.

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