Heteroclinic Cycles Imply Chaos and Are Structurally Stable
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 impl...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6647132 |
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doaj-0abe6c9fc73c47b59c123493d6a6c5872021-06-07T02:12:42ZengHindawi LimitedDiscrete Dynamics in Nature and Society1607-887X2021-01-01202110.1155/2021/6647132Heteroclinic Cycles Imply Chaos and Are Structurally StableXiaoying Wu0School of Financial Mathematics and StatisticsThis 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 ℝn, 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.http://dx.doi.org/10.1155/2021/6647132 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xiaoying Wu |
| spellingShingle |
Xiaoying Wu Heteroclinic Cycles Imply Chaos and Are Structurally Stable Discrete Dynamics in Nature and Society |
| author_facet |
Xiaoying Wu |
| author_sort |
Xiaoying Wu |
| title |
Heteroclinic Cycles Imply Chaos and Are Structurally Stable |
| title_short |
Heteroclinic Cycles Imply Chaos and Are Structurally Stable |
| title_full |
Heteroclinic Cycles Imply Chaos and Are Structurally Stable |
| title_fullStr |
Heteroclinic Cycles Imply Chaos and Are Structurally Stable |
| title_full_unstemmed |
Heteroclinic Cycles Imply Chaos and Are Structurally Stable |
| title_sort |
heteroclinic cycles imply chaos and are structurally stable |
| publisher |
Hindawi Limited |
| series |
Discrete Dynamics in Nature and Society |
| issn |
1607-887X |
| publishDate |
2021-01-01 |
| description |
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 ℝn, 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. |
| url |
http://dx.doi.org/10.1155/2021/6647132 |
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AT xiaoyingwu heterocliniccyclesimplychaosandarestructurallystable |
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