Heteroclinic Cycles Imply Chaos and Are Structurally Stable

Xiaoying Wu and Abdul Qadeer Khan

Discrete Dynamics in Nature and Society, 2021, vol. 2021, 1-7

Abstract: 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 ℠n, then g has heteroclinic cycles with h−gC1 being sufficiently small. The results demonstrate C1 structural stability of heteroclinic cycles. In the end, two examples are given to illustrate our theoretical results and applications.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:6647132

DOI: 10.1155/2021/6647132

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