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Fuchen Zhang, Ping Zhou, Jin Qin, Chunlai Mu, Fei Xu. DYNAMICS OF A GENERALIZED LORENZ-LIKE CHAOS DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1577-1587. doi: 10.11948/20200309
Citation: Fuchen Zhang, Ping Zhou, Jin Qin, Chunlai Mu, Fei Xu. DYNAMICS OF A GENERALIZED LORENZ-LIKE CHAOS DYNAMICAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1577-1587. doi: 10.11948/20200309
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DYNAMICS OF A GENERALIZED LORENZ-LIKE CHAOS DYNAMICAL SYSTEMS

  • 1.

    Mathematical Postdoctoral station, School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

  • 2.

    Chongqing Key Laboratory of Social Economy and Applied Statistics, College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China

  • 3.

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

  • 4.

    School of Mathematics, Zunyi Normal University, Zunyi 563006, China

  • 5.

    College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China

  • 6.

    Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

  • Corresponding author: Email: zhangfuchen1983@163.com(F. Zhang) 
  • Fund Project: The authors were supported by Chongqing Postdoctoral Science Foundation Special Funded Project (No. Xm2017174), China Postdoctoral Science Foundation (No. 2016M590850), National Natural Science Foundation of China (No. 11871122), the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Nos. KJQN201800818, KJCX2020037), the Research Fund of Chongqing Technology and Business University (Nos. 1952012, 1952026, 1951075), the Program for Chongqing Key Laboratory of Social Economy and Applied Statistics (No. ZDPTTD201909) and Cooperative program of Guizhou Provincial Department of science and technology (No. Qian Ke he LH [2015] No. 7042)
    Abstract

  • In this work, a new seven-parameter Lorenz-like chaotic system is presented and discussed by combining nonlinear dynamical systems theory with computer simulation. The existence of the ultimate bound set and global exponential attractive set of this chaotic system is proved by using Lyapunov's direct method. A family of analytic mathematical expression of the ultimate bound sets and global exponential attractive sets involving two parameters are obtained, respectively. Meanwhile, the volumes of the ultimate bound set and global exponential attractive set are obtained, respectively. Numerical simulations are conducted which validates the correctness of the proposed theoretical analysis.
    MSC: 34D06, 34H10
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