Stability of synchronous chaos and on-off intermittency in coupled map lattices

In this paper we consider the stability of synchronous chaos in lattices of coupled N-dimensional maps. For global coupling, we derive explicit conditions for computing the parameter values at which the synchronous chaotic attractor becomes unstable and bifurcates into asynchronous chaos. In particular, we show that after the bifurcation one generally observes on-off intermittency, a process in which the entire system evolves nearly synchronously (but chaotically) for long periods of time, which are interrupted by brief bursts away from synchrony. For nearest-neighbor coupled systems, however, we show that the stability of the synchronous chaotic state is a function of the system size. In particular, for large systems, we will not be able to observe synchronous chaos. We derive a condition relating the local map's largest Lyapunov exponent to the maximal system size under which one can still observe synchronous chaos and on-off intermittency. Other issues related to the characterization of on-off intermittent signals are also discussed.