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arXiv · 1509.07277

Asymptotic stability of pseudo-simple heteroclinic cycles in R^4

Olga Podvigina·Pascal Chossat
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Abstract

Robust heteroclinic cycles in equivariant dynamical systems in R^4 have been a subject of intense scientific investigation because, unlike heteroclinic cycles in R^3, they can have an intricate geometric structure and complex asymptotic stability properties that are not yet completely understood. In a recent work, we have compiled an exhaustive list of finite subgroups of O(4) admitting the so-called simple heteroclinic cycles, and have identified a new class which we have called pseudo-simple heteroclinic cycles. By contrast with simple heteroclinic cycles, a pseudo-simple one has at least one equilibrium with an unstable manifold which has dimension 2 due to a symmetry. Here, we analyse the dynamics of nearby trajectories and asymptotic stability of pseudo-simple heteroclinic cycles in R^4.

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Olga Podvigina, Pascal Chossat. 2015-09-24. Asymptotic stability of pseudo-simple heteroclinic cycles in R^4. https://doi.org/10.1007/s00332-016-9335-4

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