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Author:

Wei, Zhouchao (Wei, Zhouchao.) | Li, Yingying (Li, Yingying.) | Sang, Bo (Sang, Bo.) | Liu, Yongjian (Liu, Yongjian.) | Zhang, Wei (Zhang, Wei.)

Indexed by:

EI Scopus SCIE

Abstract:

This paper shows some examples of chaotic systems for the six types of only one hyperbolic equilibrium in changed chameleon-like chaotic system. Two of the six cases have hidden attractors. By adjusting the parameters in the system and controlling the stability of only one equilibrium, we can further obtain chaos with four kinds of conditions: (1) index-0 node; (2) index-3 node; (3) index-0 node foci; (4) index-3 node foci. Based on the method of focus quantities, we study three limit cycles (the outmost and inner cycles are stable, and the intermediate cycle is unstable) bifurcating from an isolated Hopf equilibrium. In addition, one periodic solution can be obtained from a nonisolated zero-Hopf equilibrium. The system may help us in better understanding, revealing an intrinsic relationship of the global dynamical behaviors with the stability of equilibrium point, especially hidden chaotic attractors.

Keyword:

zero-Hopf bifurcation degenerate Hopf bifurcation stable equilibrium Hidden chaos multistability

Author Community:

  • [ 1 ] [Wei, Zhouchao]China Univ Geosci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China
  • [ 2 ] [Li, Yingying]China Univ Geosci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China
  • [ 3 ] [Sang, Bo]Liaocheng Univ, Sch Math Sci, Liaocheng 252059, Shandong, Peoples R China
  • [ 4 ] [Liu, Yongjian]Yulin Normal Univ, Guangxi Coll & Univ Key Lab Complex Syst Optimiza, Yulin 537000, Guangxi, Peoples R China
  • [ 5 ] [Zhang, Wei]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China

Reprint Author's Address:

  • [Wei, Zhouchao]China Univ Geosci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China

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Source :

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

ISSN: 0218-1274

Year: 2019

Issue: 7

Volume: 29

2 . 2 0 0

JCR@2022

ESI Discipline: MATHEMATICS;

ESI HC Threshold:54

JCR Journal Grade:2

Cited Count:

WoS CC Cited Count: 38

SCOPUS Cited Count: 42

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 15

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