Nonasymptotically stable attractors in O(2) mode interactions

Normal Forms and Homoclinic Chaos (W. Langford and W. Nagata eds.) Fields Institute Communications 4, Amer. Math. Soc., Providence, RI, 1995, 219-232

Martin Krupa and Ian Melbourne


Heteroclinic cycles are a natural source of nonasymptotically stable attractors in systems with symmetry. In this paper, stability properties are completely classified for a large class of heteroclinic cycles. In particular, we establish the existence of several nonasymptotically stable attractors in codimension two mode interactions with O(2) symmetry, in the process explaining the results of some numerical experiments. In the Hopf/Hopf mode interaction we show that two heteroclinic cycles can coexist as nonasymptotically stable attractors.

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