Asymptotic Stability of Pseudo-simple Heteroclinic Cycles in $${\mathbb R}^4$$ R 4
| Autor: | Pascal Chossat, Olga Podvigina |
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| Rok vydání: | 2016 |
| Předmět: |
Physics
Pure mathematics Mathematics::Dynamical Systems Dynamical systems theory Applied Mathematics 010102 general mathematics Dimension (graph theory) General Engineering Heteroclinic cycle 01 natural sciences Manifold Nonlinear Sciences::Chaotic Dynamics Exponential stability Simple (abstract algebra) Modeling and Simulation 0103 physical sciences Equivariant map 010307 mathematical physics 0101 mathematics Symmetry (geometry) |
| Zdroj: | Journal of Nonlinear Science. 27:343-375 |
| ISSN: | 1432-1467 0938-8974 |
| DOI: | 10.1007/s00332-016-9335-4 |
| Popis: | 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 $${\mathbb R}^4$$ . |
| Databáze: | OpenAIRE |
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