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

^*Corresponding author for this work

School of Mathematical Sciences

Peking University
Anshan Normal University

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English
Pages (from-to)	4209-4216
Number of pages	8
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	70
Issue number	12
DOIs	https://doi.org/10.1016/j.na.2008.09.018
State	Published - 15 Jun 2009

Keywords

Bifurcation
Crisis
Generalized Ushiki map
Intermittency
Marotto chaos

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10.1016/j.na.2008.09.018

Cite this

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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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AU - Liu, Bing

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N2 - 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.

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

UR - https://www.scopus.com/pages/publications/63449140038

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DO - 10.1016/j.na.2008.09.018

M3 - 文章

AN - SCOPUS:63449140038

SN - 0362-546X

VL - 70

SP - 4209

EP - 4216

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -

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

Abstract

Keywords

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