A Resolution of the Puzzle of the Posi-nega Switch Mechanism in the Globally Coupled Map Lattice

Abstract

We revisit the globally coupled map lattice (GCML). We use a family of universal 'curves of balance' between two conflicting tendencies in the model- the randomness in each map and the coherence due to an averaging interaction - and we locate the posi-nega switch region in the parameter space of the model. We clarify the mechanism of a basic posi-nega switch in the two-cluster regime, which guarantees no mixing of maps across their mean field in the chaotic transient process. We stress that a special attention must be paid for rounding-off errors; otherwise, there fatally occurs an artifitial numerical degeneracy of maps in a cluster due to a highly negative Lyapunov exponent of the clustor attractor.