Phase synchronization of two-dimensional lattices of coupled chaotic maps

Phase synchronized states can emerge in the collective behavior of an ensemble of two-dimensional chaotic coupled map lattices, due to a nearest-neighbor interaction. A definition of phase is given for iterated systems, which corresponds to the definition of phase in continuous systems. The transition to phase synchronization is characterized in an ensemble of lattices of logistic maps, in terms of the phase synchronization ratio, the average abnormal ratio, and conditional Lyapunov exponents. The largest Lyapunov exponent of the global system λ_max depends on both the number of coupled maps and the coupling strength. If the number of coupled maps is over some threshold, λ_max depends only on the coupling strength. The approach of nearest-neighbor coupling is robust against a small difference in the map parameters.