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Complex Dynamical Behaviors of Lorenz-Stenflo Equations

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  • Fuchen Zhang

    (Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
    Mathematical Postdoctoral station, College of Mathematics and Statistics, Southwest University, Chongqing 400716, China)

  • Min Xiao

    (College of Automation, Nanjing University of Posts and Telecommunications, Nanjing 210003, China)

Abstract

A mathematical chaos model for the dynamical behaviors of atmospheric acoustic-gravity waves is considered in this paper. Boundedness and globally attractive sets of this chaos model are studied by means of the generalized Lyapunov function method. The innovation of this paper is that it not only proves this system is globally bounded but also provides a series of global attraction sets of this system. The rate of trajectories entering from the exterior of the trapping domain to its interior is also obtained. Finally, the detailed numerical simulations are carried out to justify theoretical results. The results in this study can be used to study chaos control and chaos synchronization of this chaos system.

Suggested Citation

  • Fuchen Zhang & Min Xiao, 2019. "Complex Dynamical Behaviors of Lorenz-Stenflo Equations," Mathematics, MDPI, vol. 7(6), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:513-:d:237459
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    References listed on IDEAS

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    1. Wang, Xingyuan & Wang, Mingjun, 2008. "A hyperchaos generated from Lorenz system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(14), pages 3751-3758.
    2. Wu, Xiangjun & Zhu, Changjiang & Kan, Haibin, 2015. "An improved secure communication scheme based passive synchronization of hyperchaotic complex nonlinear system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 201-214.
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    Cited by:

    1. Chih-Hsueh Lin & Guo-Hsin Hu & Jun-Juh Yan, 2020. "Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    2. Samia Rezzag & Fuchen Zhang, 2022. "On the Dynamics of New 4D and 6D Hyperchaotic Systems," Mathematics, MDPI, vol. 10(19), pages 1-10, October.

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