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Bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity

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Abstract

In this paper, the bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity are investigated via the analytical methods and numerical calculations. We discuss the local stabilities of equilibrium points and its bifurcations depending on parameters. The predicted bifurcations of periodic orbits including flip bifurcation, fold bifurcation and symmetry-breaking bifurcation are investigated. The accurate relations between parameters are established to identify the type of bifurcation appearing in system efficiently. Such simple system has very abundant dynamical behaviors, including period-doubling cascades route to chaos, intermittency regime, antimonotonicity and boundary crisis. The coexisting dynamics is confirmed effectively by using basins of attraction, bifurcation diagram, Lyapunov exponent spectrum and phase portraits. The research reveals the richness and complexity of potential stable states to which this chaotic hyperjerk system can evolve and offers flexibility in realization of various applications including secure communications.

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Acknowledgements

The research project is supported by National Natural Science Foundation of China (Grant Nos. 11772007, 11372014, 11832002, 11290152) and also supported by Beijing Natural Science Foundation (Grant Nos. 1172002, Z180005), the International Science and Technology Cooperation Program of China (Grant No. 2014DFR61080), Beijing Key Laboratory on Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, P. R. China.

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Authors and Affiliations

  1. Interdisciplinary Research Institute, Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Lishuang Jiang & Jing Li

  2. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, China

    Wei Zhang

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  1. Lishuang Jiang
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  2. Jing Li
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Correspondence to Jing Li.

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Jiang, L., Li, J. & Zhang, W. Bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity. Eur. Phys. J. Plus 135, 767 (2020). https://doi.org/10.1140/epjp/s13360-020-00786-x

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