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 bo...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.展开更多
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)+2 种基金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)
文摘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.
