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A New Hyperchaotic Complex System With Parametric Attractors

Author

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  • FANGFANG ZHANG

    (Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China†College of Control Science and Engineering, Shandong University, Jinan 250061, P. R. China)

  • ZHENGFENG LI

    (Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China)

  • KAI SUN

    (Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China)

  • XUE ZHANG

    (Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China)

  • PENG JI

    (Department of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, P. R. China)

Abstract

We propose a new hyperchaotic complex system. The hyperchaotic complex system has a distinctive chaotic attractor, which is called butterfly-like attractor. We find that the state of the system has a complex evolution process with the change of parameters, and the system will produce at least two kinds of attractors, which we call parametric attractors. We systematically study the mechanics, symmetry, dissipation, Lyapunov exponents and Poincaré maps of the hyperchaotic complex system. We extend the hyperchaotic complex system to fractional order, and discuss the influence of order and parameters’ change on fractional order new hyperchaotic system, and compare it with integer order. What is interesting is that there exist parametric attractors in both integer order and fractional order of the new system. Based on the integer order and fractional order, we further analyze the new hyperchaotic complex system of hybrid order, propose the definition of complex chaotic family and carry out mechanical analysis.

Suggested Citation

  • Fangfang Zhang & Zhengfeng Li & Kai Sun & Xue Zhang & Peng Ji, 2021. "A New Hyperchaotic Complex System With Parametric Attractors," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(07), pages 1-20, November.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:07:n:s0218348x21502303
    DOI: 10.1142/S0218348X21502303
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    Cited by:

    1. Zhang, Zefeng & Huang, Lilian & Liu, Jin & Guo, Qiang & Du, Xiuli, 2022. "A new method of constructing cyclic symmetric conservative chaotic systems and improved offset boosting control," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Zhang, Fangfang & Zhang, Shuaihu & Chen, Guanrong & Li, Chunbiao & Li, Zhengfeng & Pan, Changchun, 2022. "Special attractors and dynamic transport of the hybrid-order complex Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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