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Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, P. R. China

Department of Electrical and Electronics Engineering, Faculty of Technology, Sakarya University, 54187 Serdivan, Sakarya, Turkey

E-mail Address: aakgul@sakarya.edu.tr

Corresponding author.

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Xiao-Wen Zhao

School of Mathematics, Hefei University of Technology, Hefei 230009, P. R. China

E-mail Address: zhaoxiaowen1983@163.com

Corresponding author.

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Huiqin Pei

School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, P. R. China

E-mail Address: peihuiqinnx@126.com

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https://doi.org/10.1142/S0218127417501425Cited by:66 (Source: Crossref)

Abstract

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

Keywords:

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