Bifurcation analysis of the Henon map

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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Main Authors: Erik Mosekilde, Zhanybai T. Zhusubaliyev, Vadim N. Rudakov, Evgeniy A. Soukhterin
Format: Article
Language:English
Published: Hindawi Limited 2000-01-01
Series:Discrete Dynamics in Nature and Society
Subjects:
Hénon two-dimensional mapping; Chaos; Bifurcations; Branching pattern.
Online Access:http://dx.doi.org/10.1155/S1026022600000534
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spelling doaj-407efe8c74d54896a77aeb87ed95a6062020-11-24T23:37:59ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2000-01-015320322110.1155/S1026022600000534Bifurcation analysis of the Henon mapErik Mosekilde0Zhanybai T. Zhusubaliyev1Vadim N. Rudakov2Evgeniy A. Soukhterin3Center for Chaos and Turbulence Studies, Department of Physics, Technical University of Denmark, Lyngby 2800, DenmarkKursk State Technical University, Department of Computer Science, 50 Years of October Street, 94, Kursk 305040, RussiaKursk State Technical University, Department of Computer Science, 50 Years of October Street, 94, Kursk 305040, RussiaCenter for Chaos and Turbulence Studies, Department of Physics, Technical University of Denmark, Lyngby 2800, DenmarkDivision 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.http://dx.doi.org/10.1155/S1026022600000534Hénon two-dimensional mapping; Chaos; Bifurcations; Branching pattern.
collection DOAJ
language English
format Article
sources DOAJ
author Erik Mosekilde
Zhanybai T. Zhusubaliyev
Vadim N. Rudakov
Evgeniy A. Soukhterin
spellingShingle Erik Mosekilde
Zhanybai T. Zhusubaliyev
Vadim N. Rudakov
Evgeniy A. Soukhterin
Bifurcation analysis of the Henon map
Discrete Dynamics in Nature and Society
Hénon two-dimensional mapping; Chaos; Bifurcations; Branching pattern.
author_facet Erik Mosekilde
Zhanybai T. Zhusubaliyev
Vadim N. Rudakov
Evgeniy A. Soukhterin
author_sort Erik Mosekilde
title Bifurcation analysis of the Henon map
title_short Bifurcation analysis of the Henon map
title_full Bifurcation analysis of the Henon map
title_fullStr Bifurcation analysis of the Henon map
title_full_unstemmed Bifurcation analysis of the Henon map
title_sort bifurcation analysis of the henon map
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2000-01-01
description 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.
topic Hénon two-dimensional mapping; Chaos; Bifurcations; Branching pattern.
url http://dx.doi.org/10.1155/S1026022600000534
work_keys_str_mv AT erikmosekilde bifurcationanalysisofthehenonmap
AT zhanybaitzhusubaliyev bifurcationanalysisofthehenonmap
AT vadimnrudakov bifurcationanalysisofthehenonmap
AT evgeniyasoukhterin bifurcationanalysisofthehenonmap
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