Transitions to Intermittency and Collective Behavior in Randomly Coupled Map Networks

We study the collective behavior in a random network of coupled Chaté Manneville (CM) maps where the relevant variables are the connectivity k, coupling ε, and the governing parameter of map r. We show that for some interval of their values at least a considerable fraction of network sites display a spatio-temporal intermittency. Within the intermittency window, the system exhibits a complex collective periodic behavior. The detailed behavior crucially depends upon the topology of the random graph spanning the network. Our approach is based on the thermodynamic formalism (TD) and random graph theory.