Phase Clustering and Collective Behaviors in Globally Coupled Map Lattices due to mean Filed Effects

Abstract

We describe the emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean eld interaction. This kind of interaction is responsible for the appearence of a collective state, wherein the mean eld evolution of each lattice undergoes a periodic behavior in space. We analyze the transition to such a state in an ensemble of one-dimensional lattices of logistic maps, showing that the resulting behavior cooperatively maximizes the energy of the mean eld activity.