Intermittency in coupled maps

Abstract

Using a renormalization method, we study the critical behavior for intermittency in two coupled one-dimensional (1D) maps. We find two fixed maps of the renormalization transformation. They all have common relevant eigenvalues associated with scaling of the control parameter of the uncoupled 1D map. However, the relevant ``coupling eigenvalues'' associated with coupling perturbations vary depending on the fixed maps. It is also found that the two fixed maps are associated with the critical behavior in the vicinity of a critical line segment. One fixed map with no relevant coupling eigenvalues governs the critical behavior at interior points of the critical line segment, while the other one with relevant coupling eigenvalues governs the critical behavior at both ends. The results of the two coupled 1D maps are also extended to many globally-coupled 1D maps, in which each 1D map is coupled to all the other ones with equal strength.