Globally exponentially attractive sets of the family of Lorenz systems  

作　　者：LIAO XiaoXin FU YuLi XIE ShengLi YU Pei 

机构地区：[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

出　　处：《Science in China(Series F)》2008年第3期283-292,共10页中国科学（F辑英文版）

基　　金：Supported partly by the National Natural Science Foundation of China (Grant Nos. 60474011 and 60274007);the National Natural Science Foun-dation 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);the Natural Science and Engineering Re-search Council of Canada (Grant No. R2686A02)

摘　　要：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.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.

关 键 词：the family of Lorenz systems globally exponentially attractive set Lagrange stability generalized Lyapunov function 

分 类 号：O17[理学—数学]