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A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes

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  • Ping Zhou
  • Meihua Ke

Abstract

Based on the 3D autonomous continuous Lü chaotic system, a new 3D autonomous continuous chaotic system is proposed in this paper, and there are coexisting chaotic attractors in the 3D autonomous continuous chaotic system. Moreover, there are no overlaps between the coexisting chaotic attractors; that is, there are two isolated chaotic attractors (in this paper, named “positive attractor” and “negative attractor,” resp.). The “positive attractor” and “negative attractor” depend on the distance between the initial points (initial conditions) and the unstable equilibrium points. Furthermore, by means of topological horseshoes theory and numerical computation, the topological horseshoes in this 3D autonomous continuous system is found, and the topological entropy is obtained. These results indicate that the chaotic attractor emerges in the new 3D autonomous continuous system.

Suggested Citation

  • Ping Zhou & Meihua Ke, 2017. "A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes," Complexity, Hindawi, vol. 2017, pages 1-7, November.
    • Handle: RePEc:hin:complx:4037682
    DOI: 10.1155/2017/4037682
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    References listed on IDEAS

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    1. Ma, Jun & Wu, Fuqiang & Ren, Guodong & Tang, Jun, 2017. "A class of initials-dependent dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 65-76.
    2. Yu Feng & Zhouchao Wei & Uğur Erkin Kocamaz & Akif Akgül & Irene Moroz, 2017. "Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria," Complexity, Hindawi, vol. 2017, pages 1-11, May.
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    Cited by:

    1. Liu, Zhilong & Ma, Jun & Zhang, Ge & Zhang, Yin, 2019. "Synchronization control between two Chua′s circuits via capacitive coupling," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 94-106.
    2. Nwachioma, Christian & Pérez-Cruz, J. Humberto, 2021. "Analysis of a new chaotic system, electronic realization and use in navigation of differential drive mobile robot," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Dong, Chengwei & Liu, Huihui & Jie, Qi & Li, Hantao, 2022. "Topological classification of periodic orbits in the generalized Lorenz-type system with diverse symbolic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Ping Zhou & Meihua Ke & Peng Zhu, 2018. "A Fractional-Order System with Coexisting Chaotic Attractors and Control Chaos via a Single State Variable Linear Controller," Complexity, Hindawi, vol. 2018, pages 1-7, June.

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