Coupling effect on the occurrence of partial synchronization in four coupled chaotic systems

초록

We study the coupling effect on the occurrence of partial synchronization in four coupled one-dimensional maps by varying a parameter w (0 <= w <= 1) which tunes the "weight" in the next-nearest-neighbor coupling from the local nearest-neighbor coupling (w = 0) to the global coupling (w = 1). As the coupling parameter a decreases and passes a threshold value epsilon*, the fully synchronized attractor on the diagonal becomes transversely unstable via a blowout bifurcation, and then a partially synchronized or completely desynchronized attractor appears depending on the value of w. For the case of local coupling (w = 0), partial synchronization occurs on an invariant plane. However, as w increases and passes a threshold value w*, a transition from partial synchronization to complete desynchronization takes place. Thus, for w* < w <= 1, a fully desynchronized attractor, occupying a finite four-dimensional volume, appears. The dynamical mechanism for the occurrence of partial synchronization is investigated through competition between the laminar and bursting components of the intermittent two-cluster state born via the blowout bifurcation. Another type of partial synchronization, which occurs through a dynamical stabilization of an unstable orbit, is also discussed for both the local and global couplings. These results for the partial synchronization are also confirmed in a system of four coupled pendula. (c) 2006 Elsevier B.V. All rights reserved.

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