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Dynamical Analysis of the Generalized Lorenz Systems

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Abstract

In this paper, global attractive sets of the generalized Lorenz system are studied according to Lyapunov stability theory and optimization theory. The method of constructing Lyapunov functions applied to the former chaotic dynamical systems is not applicable to the generalized Lorenz system. We overcome this difficulty by adding a cross term to the Lyapunov functions of the generalized Lorenz system.

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Acknowledgments

This research is supported by the National Natural Science Foundation of China (Grant Nos: 11426047, 11501064), the Basic and Advanced Research Project of CQCSTC (Grant No: cstc2014jcyjA00040), Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJ1500605), and the Research Fund of Chongqing Technology and Business University (Grant No: 2014-56-11).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Fuchen Zhang

  2. College of Electronic and Information Engineering, Southwest University, Chongqing, 400716, People’s Republic of China

    Xiaofeng Liao

  3. International Business School, Chongqing Technology and Business University, Chongqing, 400067, People’s Republic of China

    Guangyun Zhang

  4. College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, People’s Republic of China

    Chunlai Mu

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  1. Fuchen Zhang
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  2. Xiaofeng Liao
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  3. Guangyun Zhang
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  4. Chunlai Mu
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Correspondence to Fuchen Zhang.

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Zhang, F., Liao, X., Zhang, G. et al. Dynamical Analysis of the Generalized Lorenz Systems. J Dyn Control Syst 23, 349–362 (2017). https://doi.org/10.1007/s10883-016-9325-8

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  • DOI: https://doi.org/10.1007/s10883-016-9325-8

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