Globally exponentially attractive sets of the family of Lorenz systems. (English) Zbl 1148.37025

Liao, Xiaoxin; Fu, Yuli; Xie, Shengli; Yu, Pei

Sci. China, Ser. F. 51, No. 3, 283-292 (2008).

Summary: 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, \(b \rightarrow 1^{+}\) and \(a \rightarrow 0^{+}\), for which the previous methods failed, have been solved using a unified formula.

MSC:

37D45	Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37C10	Dynamics induced by flows and semiflows
34C28	Complex behavior and chaotic systems of ordinary differential equations
34D45	Attractors of solutions to ordinary differential equations

Keywords:

family of Lorenz systems; globally exponentially attractive set; Lagrange stability; generalized Lyapunov function

Software:

RODES

References:

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