  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.
