On the study of globally exponentially attractive set of a general chaotic system. (English) Zbl 1221.37072
Summary: We prove that there exists globally exponential attractive and positive invariant set for a general chaotic system, which does not belong to the known Lorenz system, or the Chen system, or the Lorenz family. We show that all the solution orbits of the chaotic system are ultimately bounded with exponential convergent rates and the convergent rates are explicitly estimated. The method given in this paper can be applied to study other chaotic systems.
MSC:
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
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