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Author:

Wei, Zhouchao (Wei, Zhouchao.) | Viet-Thanh Pham (Viet-Thanh Pham.) | Kapitaniak, Tomasz (Kapitaniak, Tomasz.) | Wang, Zhen (Wang, Zhen.)

Indexed by:

Scopus SCIE

Abstract:

In this paper, we investigate the effect of multiple delays on the 3-D simple chaotic system with hidden chaotic attractors coexisting with one stable equilibrium by Wang and Chen. In order to investigate complex dynamics of hidden chaotic attractors with multiple delays, we choose and as bifurcating parameters and consider the stability of equilibrium and the existence of Hopf bifurcations. Some explicit formulas for determining the direction of bifurcations and the stability of bifurcating periodic solutions are obtained by using normal form theory and center manifold theory. The numerical simulations are performed to support the correctness and effectiveness of the analytical results. The effect of multiple delays can be applied to the chaotic system only with one stable node-foci for the purpose of control and anti-control of hidden chaos by delayed switchover. Furthermore, to reach deep and clear understanding of the dynamics of such hidden attractors, circuit implementation of the multiple time-delay system is analyzed using the PSpice.

Keyword:

Hopf bifurcation Multiple delays Stable node-foci Periodic solution Hidden attractor

Author Community:

  • [ 1 ] [Wei, Zhouchao]China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China
  • [ 2 ] [Wei, Zhouchao]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China
  • [ 3 ] [Wei, Zhouchao]Univ Oxford, Math Inst, Oxford OX2 6GG, England
  • [ 4 ] [Wei, Zhouchao]Tech Univ Lodz, Div Dynam, Stefanowskiego 1-15, PL-90924 Lodz, Poland
  • [ 5 ] [Kapitaniak, Tomasz]Tech Univ Lodz, Div Dynam, Stefanowskiego 1-15, PL-90924 Lodz, Poland
  • [ 6 ] [Viet-Thanh Pham]Hanoi Univ Sci & Technol, Sch Elect & Telecommun, 01 Dai Co Viet, Hanoi, Vietnam
  • [ 7 ] [Wang, Zhen]Xijing Univ, Dept Appl Sci, Xian 710123, Peoples R China

Reprint Author's Address:

  • [Wei, Zhouchao]China Univ Geosci, Sch Math & Phys, Wuhan 430074, Peoples R China;;[Wei, Zhouchao]Beijing Univ Technol, Coll Mech Engn, Beijing 100124, Peoples R China;;[Wei, Zhouchao]Univ Oxford, Math Inst, Oxford OX2 6GG, England;;[Wei, Zhouchao]Tech Univ Lodz, Div Dynam, Stefanowskiego 1-15, PL-90924 Lodz, Poland

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Source :

NONLINEAR DYNAMICS

ISSN: 0924-090X

Year: 2016

Issue: 3

Volume: 85

Page: 1635-1650

5 . 6 0 0

JCR@2022

ESI Discipline: ENGINEERING;

ESI HC Threshold:166

CAS Journal Grade:1

Cited Count:

WoS CC Cited Count: 69

SCOPUS Cited Count: 75

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 5

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