Phenomenology of Globally Coupled Map Lattice and its Extension
  We revisit the globally coupled map lattice (GCML) and also propose a new extended globally coupled map lattice (EGCML) with an inverse power law interaction. In GCML we clarify the mechanism of the basic posi-nega switch in the two-cluster regime. We show that there is a natural mechanism in GCML which guarantees no mixing of maps across their mean field in the chaotic transient process. In the turbulent regime of GCML there is a prominent period three window. In the correlator analysis we also find a remnant of periodic motion of quasi-clusters with high rate mixing almost everywhere in the turbulent regime of the large-size GCML. The so-called hidden coherence is the most modest remnant. The EGCML shares the same intriguing properties with GCML and exhibits an amazing spatial cluster formation during the chaotic transient process. An analytic approach is proposed which relates the periodicity manifestation in the turbulent regime of GCML to the periodic window of a single logistic map. 
Tokuzo Shimada