Spatiotemporal periodic and chaotic patterns in a two-dimensional coupled map lattice system

The pattern dynamics of a two-dimensional coupled map lattice system is studied using both analytical and numerical calculations. Two interesting spatiotemporal periodic patterns are solved analytically. Their stability boundaries for small system size are obtained by linear stability analysis. As the system sizes mismatch the spatial periodicity of the patterns, a frozen random chaotic defect cluster and a slow random propagated chaotic defect string appear.