On the occurrence of partial synchronization in unidirectionally coupled maps

초록

We study three unidirectionally coupled one-dimensional unimodal maps by changing the order alpha (1 <= alpha <= 2) of the local maximum. A fully synchronized chaotic attractor on the diagonal becomes transversely unstable via a blowout bifurcation; then, partial synchronization or complete desynchronization occurs depending on the value of alpha. For the quadratic case with alpha = 2, a partially synchronized chaotic attractor appears on an invariant plane. However, as the parameter alpha decreases and passes a threshold value alpha*, a transition from partial synchronization to complete desynchronization takes place. Hence, for 1 <= alpha <= alpha*, a completely desynchronized chaotic attractor occupies a finite three-dimensional volume because the two-cluster state on the invariant plane, born via the blowout bifurcation, is transversely unstable. The mechanism for the occurrence of partial synchronization is discussed through competition between the laminar and the bursting components of the intermittent two-cluster state born at the blowout bifurcation.

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