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Chen, Yuanlong; Wu, Xiaoying

doi:10.1016/j.jmaa.2019.123823

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…Based on the research of Marotto, Shi and Chen raised the concept of snapback repellers in Banach spaces and complete metric spaces [14,15]. As is well known, some homoclinic and heteroclinic cycles imply chaos in dynamical systems [6,16]. Lin and Chen introduced the new chaotic criteria of heteroclinic repellers in R n [17].…”

Section: Introductionmentioning

confidence: 99%

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Heteroclinic Cycles Imply Chaos and Are Structurally Stable

2021

Discrete Dynamics in Nature and Society

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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 ℝ n , then g has heteroclinic cycles with h − g 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.

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Section: Introductionmentioning

confidence: 99%

“…Chen and Li provided a sufficient condition of a high-dimensional difference equation having symbolic embedding for enough small C 1 perturbations [22]. In 2020, Chen and Wu et al showed that the system with heteroclinic repellers has the structural stability in [4,16].…”

Section: Introductionmentioning

confidence: 99%

Heteroclinic Cycles Imply Chaos and Are Structurally Stable

2021

Discrete Dynamics in Nature and Society

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A new chaotic criterion and its structural stability in Banach space

Wu,

Chen

2025

Journal of Mathematical Analysis and Applications

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Persistence of Heteroclinic Cycles Connecting Repellers in Banach Spaces

2022

Journal of Mathematics

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This paper is concerned with persistence of heteroclinic cycles connecting repellers in Banach spaces. It is proved that if a map with a regular and nondegenerate heteroclinic cycle connecting repellers undergoes a small perturbation, then the perturbed map can still have a regular and nondegenerate heteroclinic cycle connecting repellers. The perturbation rang is given by an explicit positive constant according to the properties of the original map. Hence, the perturbed map and the original map are simultaneously chaotic in the sense of both Devaney and Li-Yorke. Especially, the persistence of heteroclinic cycles connecting repellers is also discussed in the Euclidean space, where the repellers can expand in different norms. Finally, three examples are provided to illustrate the validity of the theoretical results.

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The C1 persistence of heteroclinic repellers in Rn

Cited by 4 publications

References 15 publications

Heteroclinic Cycles Imply Chaos and Are Structurally Stable

Heteroclinic Cycles Imply Chaos and Are Structurally Stable

A new chaotic criterion and its structural stability in Banach space

Persistence of Heteroclinic Cycles Connecting Repellers in Banach Spaces

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