Skip to Main content Skip to Navigation
Journal articles

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 $\mathbb{R}^4$.
Document type :
Journal articles
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01286143
Contributor : Pascal Chossat <>
Submitted on : Thursday, March 10, 2016 - 5:40:07 PM
Last modification on : Monday, October 12, 2020 - 2:28:06 PM
Long-term archiving on: : Sunday, November 13, 2016 - 2:01:13 PM

File

st1509.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01286143, version 1
  • ARXIV : 1509.07277

Citation

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. ⟨hal-01286143⟩

Share

Metrics

Record views

532

Files downloads

95