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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1026-0226 1607-887X |