Phase clustering and collective behaviors in globally coupled map lattices due to mean field effects

TLDR: The emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean field interaction, is described, showing that the resulting behavior cooperatively maximizes the energy of the mean field activity.

Abstract: We describe the emergence of phase clustering and collective behaviors in an ensemble of chaotic coupled map lattices, due to a mean field interaction. This kind of interaction is responsible for the appearence of a collective state, wherein the mean field 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 field activity.