Phase synchronization and its cluster feature in two-dimensional coupled map lattices.

Due to a diffusive nearest-neighbor coupling, phase-synchronized states can emerge in two-dimensional chaotic coupled map lattices. By defining a direction phase (like a spin with up or down direction) as the direction of two sequential iterations of the logistic map, we find several novel kinds of phase synchronization which correspond to four different regions in a phase diagram. For the phase with partial phase synchronization, as the coupling strength epsilon increases to a critical threshold epsilon(c), a percolationlike transition is found in the cluster feature of the direction phases relating to the pattern formation. In addition, a scaling of the percolation probability rho approximately (epsilon-epsilon(c))(beta) with beta=2.1 is obtained. The spatial and time correlation functions of the phase clusters are also discussed.