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

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.


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


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