Mechanism of synchronization in a random dynamical system
Dong-Uk Hwang, Inbo Kim, Sunghwan Rim, Chil-Min Kim, Young-Jai Park
Abstract
The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was found. We have verified the structure of on-off intermittency in terms of a biased random walk. Furthermore, for the generalized case of the ensemble of particles, a modified definition of the size of a snapshot attractor was exploited to establish the link with a random walk. As a result, the structure of on-off intermittency in the ensemble of particles was explicitly revealed near the transition.
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