Chaotic Itinerancy Observed in Mutually Coupled Gaussian Maps
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Abstract
A one-dimensional Gaussian map defined by a Gaussian function describes a discrete-time dynamical system. Chaotic behavior can be observed in both Gaussian and logistic maps. This study analyzes the bifurcation structure corresponding to the fixed and periodic points of a coupled system comprising two Gaussian maps. The bifurcation structure of a mutually coupled Gaussian map is more complex than that of a mutually coupled logistic map. In a coupled Gaussian map, it was confirmed that after a stable fixed point or stable periodic points became unstable through the bifurcation, the points were able to recover their stability while the system parameters were changing. Moreover, we investigated a parameter region in which symmetric and asymmetric stable fixed points coexisted. Asymmetric unstable fixed point was generated by the D-type branching of a symmetric stable fixed point. The stability of the unstable fixed point could be recovered through period-doubling and tangent bifurcations. Furthermore, a homoclinic structure related to the occurrence of chaotic behavior and invariant closed curves caused by two-periodic points was observed. The mutually coupled Gaussian map was merely a two-dimensional dynamical system; however, chaotic itinerancy, known to be a characteristic property associated with high-dimensional dynamical systems, was observed. The bifurcation structure of the mutually coupled Gaussian map clearly elucidates the mechanism of chaotic itinerancy generation in the two-dimensional coupled map. We discussed this mechanism by comparing the bifurcation structures of the Gaussian and logistic maps.
Journal
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- International Journal of Bifurcation and Chaos
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International Journal of Bifurcation and Chaos 28 (4), 1830011-, 2018-04
World Scientific
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Details 詳細情報について
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- CRID
- 1050007827761969280
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- NII Article ID
- 120007144492
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- NII Book ID
- AA10810319
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- ISSN
- 02181274
- 17936551
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- Text Lang
- en
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- Article Type
- journal article
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- Data Source
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- IRDB
- Crossref
- CiNii Articles
- KAKEN