Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors

HUANG Lilian; YAO Wenju; XIANG Jianhong; WANG Linyu

doi:10.11999/JEIT201095

Volume 44 Issue 1

Jan. 2022

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Article Navigation > Journal of Electronics & Information Technology > 2022 > 44(1): 390-399

HUANG Lilian, YAO Wenju, XIANG Jianhong, WANG Linyu. Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors[J]. Journal of Electronics & Information Technology, 2022, 44(1): 390-399. doi: 10.11999/JEIT201095

Citation:

HUANG Lilian, YAO Wenju, XIANG Jianhong, WANG Linyu. Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors[J]. Journal of Electronics & Information Technology, 2022, 44(1): 390-399. doi: 10.11999/JEIT201095

Citation:

HUANG Lilian, YAO Wenju, XIANG Jianhong, WANG Linyu. Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors[J]. Journal of Electronics & Information Technology, 2022, 44(1): 390-399. doi: 10.11999/JEIT201095

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Extreme Multi-stability of a Four-dimensional Chaotic System with Infinitely Many Symmetric Homogeneous Attractors

doi: 10.11999/JEIT201095

1.
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China
2.
The Key Laboratory of Advanced Ship Communication and Information Technology, Harbin Engineering University, Harbin 150001, China

Funds: The National Natural Science Foundation of China (61203004), The Natural Science Foundation of Heilongjiang Province (F201220)，The Heilongjiang Natural Science Foundation Joint Guide Project (LH2020F022)

Received Date: 2020-12-30
Rev Recd Date: 2021-06-02

Available Online: 2021-08-26

Publish Date: 2022-01-10

Abstract

Abstract

A new four-dimensional chaotic system with extreme multi-stability based on a classic three-dimensional chaotic system is proposed. The new system has a line equilibrium point, which can generate an infinite number of symmetrical homogeneous attractors. The chaotic characteristics of the system are analyzed by phase orbit diagram and Poincaré section methods. Using phase orbit diagrams, bifurcation diagrams and Lyapunov exponent spectrum methods, the influence of initial conditions on the extreme multi-stability of the system is analyzed. The analysis shows that the system has a large initial value variation range, and the Lyapunov exponent spectrum is constant except for the zero point. In addition, the system also has centrally symmetrical discrete bifurcation diagrams. Furthermore, the relationship between the initial symmetry of the system and the symmetry of the attractor is studied, which is different from the symmetrical attractor in the existing chaotic system, which can generate an infinite number of symmetrical homogeneous attractors. Finally, circuit simulation software is used to build an analog circuit to capture the chaotic attractor of the system, and the result verifies the correctness of the numerical simulation.

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References(36)

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