Parameter Renormalization for Asymmetrically Coupled Maps

Abstract

The parameter renormalization group method proposed in the previous papers is applied to the case where the system is described by two coupled one-dimensional maps to investigate the critical behavior of periodic-doubling. Particular attention is given to the asymmetric case where the maps have different bifurcation parameters. The first-order parameter renormalization equations are found to give qualitatively correct critical behaviors by comparing with numerical simulation. Furthermore, using the parameter reduction technique, it is found that critical behaviors of the coupled maps having a set of parameters on several critical lines are equivalent to those for the corresponding uncoupled maps. *