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Hyperchaos, chaos, and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points

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Abstract

Based on three-dimensional (3D) Lü chaotic system, we introduce a four-dimensional (4D) nonlinear system with infinitely many equilibrium points. The Lyapunov-exponent spectrum is obtained for the 4D chaotic system. A hyperchaotic attractor and a chaotic attractor are emerged in this 4D nonlinear system. Furthermore, to verify the existence of hyperchaos, the chaotic dynamics of this 4D nonlinear system is also studied by means of topological horseshoe theory and numerical computation.

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Acknowledgements

We are very grateful to the reviewers for their valuable comments and suggestions. This work is supported in part by National Natural Science Foundation of China (61104150) and the Science and Technology Project of Chongqing Education Commission (No. KJ130517).

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Authors and Affiliations

  1. Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Ping Zhou

  2. Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China

    Fangyan Yang

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  1. Ping Zhou
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  2. Fangyan Yang
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Correspondence to Ping Zhou.

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Zhou, P., Yang, F. Hyperchaos, chaos, and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points. Nonlinear Dyn 76, 473–480 (2014). https://doi.org/10.1007/s11071-013-1140-0

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  • DOI: https://doi.org/10.1007/s11071-013-1140-0

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