Optimal windows of rewiring period in randomly coupled chaotic maps

The dynamics of weakly coupled chaotic maps in which the connections are rewired randomly with varying probability P and rewiring period T is investigated. In contrast to rapidly switched random links enhancing spatiotemporal regularity in strong-coupling regime, rewiring the network with certain rewiring period T contributes to the stability of synchronized cycles in a weak-coupling range, the reason of which is that unstable kink-patterns emerge and need some time steps to vanish. Furthermore, the synchronized basin size B for different period T is given. We observed an interesting phenomenon that basin B is relatively large when T is even in the range of small values of T. Finally, the synchronizing efficiency with respect to T   is discussed and we found T=2T=2 is the most efficient.