Strong persistence of an attractor and generalized partial synchronization in a coupled chaotic system |
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Authors: | Manjunath G Fournier-Prunaret D |
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Institution: | LATTIS-Institut National des Sciences Applique?es de Toulouse, Universite? de Toulouse, Toulouse, France. manju.iisc@gmail.com |
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Abstract: | It is widely believed that when two discrete time chaotic systems are coupled together then there is a contraction in the phase space (where the essential dynamics takes place) when compared with the phase space in the uncoupled case. Contrary to such a popular belief, we produce a counter example--we consider two discrete time chaotic systems both with an identical attractor A, and show that the two systems could be nonlinearly coupled in a way such that the coupled system's attractor persists strongly, i.e., it is A?×?A despite the coupling strength is varied from zero to a nonzero value. To show this, we prove robust topological mixing on A?×?A. Also, it is of interest that the studied coupled system can exhibit a type of synchronization called generalized partial synchronization which is also robust. |
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