Heteroclinic cycles imply chaos and are structurally stable
type: Item
instance of: scholarly article
title: Heteroclinic cycles imply chaos and are structurally stable
zbMATH Open document ID: 1465.37030
DOI: 10.1155/2021/6647132
author: Xiaoying Wu
published in: Discrete Dynamics in Nature and Society
publication date: 2021-07-02T00:00:00Z
review text: Summary: This paper is concerned with the chaos of discrete dynamical systems. A new concept of heteroclinic cycles connecting expanding periodic points is raised, and by a novel method, we prove an invariant subsystem is topologically conjugate to the one-side symbolic system. Thus, heteroclinic cycles imply chaos in the sense of Devaney. In addition, if a continuous differential map \(h\) has heteroclinic cycles in \(\mathbb{R}^n\), then \(g\) has heteroclinic cycles with \(\left\| h - g\right\|_{C^1}\) being sufficiently small. The results demonstrate \(C^1\) structural stability of heteroclinic cycles. In the end, two examples are given to illustrate our theoretical results and applications.
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7367235
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6647132
OpenAlex ID: W3169546001
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description: scientific article; zbMATH DE number 7367235