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On the Dynamics of New 4D and 6D Hyperchaotic Systems

Author

Listed:
  • Samia Rezzag

    (Department of Mathematics and Informatics, University Larbi Ben M’hidi, Oum-El-Bouaghi 04000, Algeria)

  • Fuchen Zhang

    (School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China)

Abstract

One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the analytical optimization, comparison principle, and generalized Lyapunov function theory, we find the ultimate bound set for a new six-dimensional hyperchaotic system and the globally exponentially attractive set for a new four-dimensional Lorenz- type hyperchaotic system. The novelty of this paper is that it not only shows the 4D hyperchaotic system is globally confined but also presents a collection of global trapping regions of this system. Furthermore, it demonstrates that the trajectories of the 4D hyperchaotic system move at an exponential rate from outside the trapping zone to its inside. Finally, some numerical simulations are shown to demonstrate the efficacy of the findings.

Suggested Citation

  • Samia Rezzag & Fuchen Zhang, 2022. "On the Dynamics of New 4D and 6D Hyperchaotic Systems," Mathematics, MDPI, vol. 10(19), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3668-:d:935000
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    References listed on IDEAS

    as
    1. Gao, Wei & Yan, Li & Saeedi, Mohammadhossein & Saberi Nik, Hassan, 2018. "Ultimate bound estimation set and chaos synchronization for a financial risk system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 154(C), pages 19-33.
    2. Fuchen Zhang & Min Xiao, 2019. "Complex Dynamical Behaviors of Lorenz-Stenflo Equations," Mathematics, MDPI, vol. 7(6), pages 1-9, June.
    3. Sun, Yeong-Jeu, 2009. "Solution bounds of generalized Lorenz chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 691-696.
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