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Globally exponentially attractive sets of the family of Lorenz systems

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Abstract

In this paper, the concept of globally exponentially attractive set is proposed and used to consider the ultimate bounds of the family of Lorenz systems with varying parameters. Explicit estimations of the ultimate bounds are derived. The results presented in this paper contain all the existing results as special cases. In particular, the critical cases, b → 1+ and a → 0+, for which the previous methods failed, have been solved using a unified formula.

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Authors and Affiliations

  1. Department of Control Science & Engineering, Huazhong University of Science & Technology, Wuhan, 430074, China

    Liao XiaoXin

  2. School of Automation, Wuhan University of Science & Technology, Wuhan, 430070, China

    Liao XiaoXin

  3. School of Electronics & Information Engineering, South China University of Technology, Guangzhou, 519640, China

    Fu YuLi & Xie ShengLi

  4. Department of Applied Mathematics, The University of Western Ontario London, Ontario, N6A 5B7, Canada

    Yu Pei

Authors
  1. Liao XiaoXin
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  2. Fu YuLi
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  3. Xie ShengLi
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  4. Yu Pei
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Corresponding author

Correspondence to Fu YuLi.

Additional information

Supported partly by the National Natural Science Foundation of China (Grant Nos. 60474011 and 60274007), the National Natural Science Foundation of China for Excellent Youth (Grant No. 60325310), the Guangdong Province Science Foundation for Program of Research Team (Grant No. 04205783), the Natural Science Fund of Guangdong Province, China (Grant No. 05006508), and the Natural Science and Engineering Research Council of Canada (Grant No. R2686A02)

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Liao, X., Fu, Y., Xie, S. et al. Globally exponentially attractive sets of the family of Lorenz systems. Sci. China Ser. F-Inf. Sci. 51, 283–292 (2008). https://doi.org/10.1007/s11432-008-0024-2

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  • DOI: https://doi.org/10.1007/s11432-008-0024-2

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