Consequences of nonlocal connections in networks of chaotic maps under threshold activated coupling

We study the effects of random nonlocal connections on networks of chaotic maps under threshold activated coupling. In threshold regimes where a large number of unsynchronized attractors occur under regular connections, we show how nonlocal rewirings yield synchronized networks. However, the dependence of the synchronized fraction on the fraction of randomized nonlocal links is typically nonmonotonic here. Further, the mean time to reach synchronization with respect to the fraction of rewiring also indicates an optimum degree of nonlocality for which synchronization is most efficiently achieved