Crisis-induced intermittency in two coupled chaotic maps: towards understanding chaotic itinerancy.
The present paper considers crisis-induced intermittency in a system composed of two coupled logistic maps. Its purpose is to clarify a bifurcation scenario generating such intermittent behaviors that can be regarded as a simple example of chaotic itinerancy. The intermittent dynamics appears immediately after an attractor-merging crisis of two off-diagonal chaotic attractors in a symmetrically coupled system. The scenario for the crisis is investigated through analyses of sequential bifurcations leading to the two chaotic attractors and successive changes in basin structures with variation of a system parameter. The successive changes of the basins are also characterized by variation of a dimension of a fractal basin boundary. A numerical analysis shows that simultaneous contacts between the attractors and the fractal basin boundary bring about the crisis and a snap-back repeller generated at the crisis produces the intermittent transitions. Furthermore, a modified scenario for intermittent behaviors in an asymmetrically coupled system is also discussed.
Tanaka
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G
Department of Complexity Science and Engineering, Graduate School of Frontier Science, The University of Tokyo, Tokyo, 113-8656, Japan.
Sanjuán
M A F
MA
Aihara
K
K