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: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S1026022600000534 |
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| _version_ | 1832549990186090496 |
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| author | Erik Mosekilde Zhanybai T. Zhusubaliyev Vadim N. Rudakov Evgeniy A. Soukhterin |
| author_facet | Erik Mosekilde Zhanybai T. Zhusubaliyev Vadim N. Rudakov Evgeniy A. Soukhterin |
| author_sort | Erik Mosekilde |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-407efe8c74d54896a77aeb87ed95a606 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-407efe8c74d54896a77aeb87ed95a6062025-02-03T06:07:56ZengWileyDiscrete 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. |
| 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. |
| title | 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_short | Bifurcation analysis of the Henon map |
| title_sort | bifurcation analysis of the henon map |
| 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 |