Study on the dynamical behaviors of a two-dimensional discrete system

Yinghui Gao; Bing Liu

doi:10.1016/j.na.2008.09.018

Study on the dynamical behaviors of a two-dimensional discrete system

Yinghui Gao^*
, Bing Liu

^*此作品的通讯作者

数学科学学院

Peking University
Anshan Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

7 引用（Scopus）

摘要

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.

源语言	英语
页（从-至）	4209-4216
页数	8
期刊	Nonlinear Analysis, Theory, Methods and Applications
卷	70
期	12
DOI	https://doi.org/10.1016/j.na.2008.09.018
出版状态	已出版 - 15 6月 2009

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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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AB - 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.

KW - Bifurcation

KW - Crisis

KW - Generalized Ushiki map

KW - Intermittency

KW - Marotto chaos

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Study on the dynamical behaviors of a two-dimensional discrete system

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