On the study of globally exponentially attractive set of a general chaotic system |
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| Authors: | P. Yu X.X. Liao |
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| Affiliation: | aDepartment of Applied Mathematics, The University of Western Ontario, London, Ont., Canada N6A 5B7;bDepartment of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China |
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| Abstract: | In this paper, 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. |
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| Keywords: | Chaotic attractor Globally exponentially attractive set Ultimate boundedness of chaos |
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