Bifurcation Analysis of the Henon Map

Division of the parameter plane for the two-dimensional Hénon mapping into domains of periodic and chaotic oscillations is studied numerically and analytically. Regularities in the occurrence of different motions and transitions are analyzed. It is shown that there are domains in the plane of parame...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2000-01, Vol.2000 (3), p.203-221
Main Authors: Mosekilde, Erik, Zhusubaliyev, Zhanybai T., Rudakov, Vadim N., Soukhterin, Evgeniy A.
Format: Article
Language:English
Subjects:
Hénon two-dimensional mapping
Chaos
Bifurcations
Branching pattern
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Summary:Division of the parameter plane for the two-dimensional Hénon mapping into domains of periodic and chaotic oscillations is studied numerically and analytically. Regularities in the occurrence of different motions and transitions are analyzed. It is shown that there are domains in the plane of parameters, where non-uniqueness of motions exists. This may lead to abrupt changes of the character of the dynamics under variation in the parameters, that is, to a sudden transition from one stable cycle to another or to chaotization of the oscillations.
ISSN:1026-0226
1607-887X
DOI:10.1155/S1026022600000534