Study on the dynamical behaviors of a two-dimensional discrete system |
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| Authors: | Yinghui Gao Bing Liu |
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| Affiliation: | aDepartment of Mathematics, Beihang University, Beijing 100083, PR China;bKey Laboratory of Mathematics, Informatics and Behavioral Semantics (Beihang University and Peking University), Ministry of Education, PR China;cDepartment of Mathematics, Anshan Normal University, Anshan, 114005, Liaoning, PR China |
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| Abstract: | The generalized Ushiki map is investigated. It is theoretically proven that there are transcritical and flip bifurcations and there exists a chaotic phenomenon in the sense of Marotto. And numerical simulations not only show the consistency with the theoretical analysis but also exhibit the complex dynamical behaviors including the period-6, 5, 3 windows, intermittency mechanics, attractor merging crisis and boundary crisis. The computation of Lyapunov exponents conforms the dynamical behaviors. |
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| Keywords: | Generalized Ushiki map Bifurcation Marotto chaos Intermittency Crisis |
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