Intermittency in coupled maps

Intermittency in coupled maps

Using a "reduced" renormalization method, we study the critical behavior for intermittency in two-coupled one-dimensional (1D) maps. Two fixed points of the reduced renormalization operator are found. 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 points. We also study the intermittency for a dissipatively coupled case and confirm the renormalization results. Finally, the results of the two coupled 1D maps are extended to many globally coupled 1D maps, in which each 1D map is coupled to all the other ones with equal strength.