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Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

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Abstract

In this paper, a new simple 4D smooth autonomous system is proposed, which illustrates two interesting rare phenomena: first, this system can generate a four-wing hyperchaotic and a four-wing chaotic attractor and second, this generation occurs under condition that the system has only one equilibrium point at the origin. The dynamic analysis approach in the paper involves time series, phase portraits, Lyapunov exponents, bifurcation diagram, and Poincaré maps, to investigate some basic dynamical behaviors of the proposed 4D system. The physical existence of the four-wing hyperchaotic attractor is verified by an electronic circuit. Finally, it is shown that the fractional-order form of the system can also generate a chaotic four-wing attractor.

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Authors and Affiliations

  1. Automation and Instruments Lab, Electrical Engineering Department, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran

    Sara Dadras & Hamid Reza Momeni

  2. Department of Electrical Engineering, Tshwane University of Technology, Pretoria, 0001, South Africa

    Guoyuan Qi

  3. Department of Physics and Electronics, Binzhou University, Binzhou, 256603, Shandong, China

    Zhong-lin Wang

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  1. Sara Dadras
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  2. Hamid Reza Momeni
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  3. Guoyuan Qi
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  4. Zhong-lin Wang
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Correspondence to Hamid Reza Momeni.

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Dadras, S., Momeni, H.R., Qi, G. et al. Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form. Nonlinear Dyn 67, 1161–1173 (2012). https://doi.org/10.1007/s11071-011-0060-0

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