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

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 ε decreases and passes a threshold value ε∗, 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∗