Globally exponentially attractive sets of the family of Lorenz systems |
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| Authors: | Liao XiaoXin Fu YuLi Xie ShengLi Yu Pei |
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| Affiliation: | (1) Department of Control Science & Engineering, Huazhong University of Science & Technology, Wuhan, 430074, China;(2) School of Automation, Wuhan University of Science & Technology, Wuhan, 430070, China;(3) School of Electronics & Information Engineering, South China University of Technology, Guangzhou, 519640, China;(4) Department of Applied Mathematics, The University of Western Ontario London, Ontario, N6A 5B7, Canada |
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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.
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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| Keywords: | the family of Lorenz systems globally exponentially attractive set Lagrange stability generalized Lyapunov function |
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