Synchronization and periodic windows in a globally coupled map lattice

A globally coupled map lattice (GCML) is an extension of a spin glass model. It consists of a large number of maps with a high degree of nonlinearity, and evolves iteratively under averaging interactions via their mean field. It exhibits various interesting phases in the conflict between randomness and coherence. We have found that even in its weak coupling regime, the effects of the periodic windows of element maps dominate the dynamics of the system, and the system forms periodic cluster attractors. This may give a clue to efficient pattern recognition by the brain. We analyze how the effect systematically depends on the distance from the periodic windows in the parameter space.