Transition to Turbulence in Coupled Maps on Hierarchical Lattices

Abstract

General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal intermittency is investigated for these geometries. Critical exponents associated to the onset of turbulence are calculated as functions of the parameters of the systems. No evidence of nontrivial collective behavior is observed in the global quantity used to characterize the spatiotemporal dynamics.