Asymptotic Stability of Pseudo-simple Heteroclinic Cycles in $\mathbb{R}^4$

Abstract : Robust heteroclinic cycles in equivariant dynamical systems in $\mathbb{R}^4$ have been a subject of intense scientific investigation because, unlike heteroclinic cycles in $\mathbb{R}^3$, 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 analyze the dynamics of nearby trajectories and asymptotic stability of pseudo-simple heteroclinic cycles in $\mathbb{R}^4$.
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  • HAL Id : hal-01286143, version 1
  • ARXIV : 1509.07277

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Olga Podvigina, Pascal Chossat. Asymptotic Stability of Pseudo-simple Heteroclinic Cycles in $\mathbb{R}^4$. Journal of Nonlinear Science, Springer Verlag, 2017, 27 (1), pp.343-375. ⟨https://link.springer.com/article/10.1007/s00332-016-9335-4⟩. ⟨hal-01286143⟩

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