Network topology and collapse of collective stable chaos

Collective stable chaos consists of the persistence of disordered patterns in dynamical spatiotemporal systems possessing a negative maximum Lyapunov exponent. We analyze the role of the topology of connectivity on the emergence and collapse of collective stable chaos in systems of coupled maps defined on a small-world networks. As local dynamics we employ a map that exhibits a period-three superstable orbit. The network is characterized by a rewiring probability $p$. We find that collective chaos is inhibited on some ranges of values of the probability $p$; instead, in these regions the system reaches a synchronized state equal to the period-three orbit of the local dynamics. Our results show that the presence of long-range interactions can induce the collapse of collective stable chaos in spatiotemporal systems.