Complex Dynamics in Generalized Hénon Map
The complex dynamics of generalized Hénon map with nonconstant Jacobian determinant are investigated. The conditions of existence for fold bifurcation, flip bifurcation, and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations....
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/270604 |
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| author | Meixiang Cai |
| author_facet | Meixiang Cai |
| author_sort | Meixiang Cai |
| collection | DOAJ |
| description | The complex dynamics of generalized
Hénon map with nonconstant Jacobian determinant are
investigated. The conditions of existence for fold bifurcation,
flip bifurcation, and Hopf bifurcation are derived by using center
manifold theorem and bifurcation theory and checked up by
numerical simulations. Chaos in the sense of Marotto's definition
is proved by analytical and numerical methods. The numerical
simulations show the consistence with the theoretical analysis and
reveal some new complex phenomena which can not be given by
theoretical analysis, such as the invariant cycles which are
irregular closed graphics, the six and forty-one coexisting
invariant cycles, and the two, six, seven, nine, ten, and thirteen
coexisting chaotic attractors, and
some kinds of strange chaotic attractors. |
| format | Article |
| id | doaj-art-63e0c9d3ffeb4d12bb1488608e50505c |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-63e0c9d3ffeb4d12bb1488608e50505c2025-02-03T01:21:18ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/270604270604Complex Dynamics in Generalized Hénon MapMeixiang Cai0Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, Hunan 410004, ChinaThe complex dynamics of generalized Hénon map with nonconstant Jacobian determinant are investigated. The conditions of existence for fold bifurcation, flip bifurcation, and Hopf bifurcation are derived by using center manifold theorem and bifurcation theory and checked up by numerical simulations. Chaos in the sense of Marotto's definition is proved by analytical and numerical methods. The numerical simulations show the consistence with the theoretical analysis and reveal some new complex phenomena which can not be given by theoretical analysis, such as the invariant cycles which are irregular closed graphics, the six and forty-one coexisting invariant cycles, and the two, six, seven, nine, ten, and thirteen coexisting chaotic attractors, and some kinds of strange chaotic attractors.http://dx.doi.org/10.1155/2015/270604 |
| spellingShingle | Meixiang Cai Complex Dynamics in Generalized Hénon Map Discrete Dynamics in Nature and Society |
| title | Complex Dynamics in Generalized Hénon Map |
| title_full | Complex Dynamics in Generalized Hénon Map |
| title_fullStr | Complex Dynamics in Generalized Hénon Map |
| title_full_unstemmed | Complex Dynamics in Generalized Hénon Map |
| title_short | Complex Dynamics in Generalized Hénon Map |
| title_sort | complex dynamics in generalized henon map |
| url | http://dx.doi.org/10.1155/2015/270604 |
| work_keys_str_mv | AT meixiangcai complexdynamicsingeneralizedhenonmap |