Multi-state coupled map lattices

We investigate a two-dimensional locally coupled map lattice (CML) with the local dynamics driven by the multi-attractor quartic map. In particular, we explore a region where two local fixed points exist, one being periodic and the other chaotic. Different sets of initial conditions such as random initial values for each site or arrangements favoring equal weights to the different local attractors were used. The system reaches different asymptotic states as the intensity or the topology of the local coupling is varied. Among the asymptotic states, we find either homogeneous collective behavior or mixtures of these with synchronized states. These states are characterized and interpreted throughout this work by the distributions of the values of the maps and by the average roughness over the lattice.