Coupled (chaotic) map lattices (CMLs) characterize the collective dynamics of a spatially distributed system whose local units are linked either locally or globally. Previous research on the dynamical behavior of CMLs, based primarily on the Perron–Frobenius operator framework, has focused mainly on the weakly coupled case. In this paper, we develop a novel geometric-combinatorial method to study the dynamical behavior of CMLs beyond the weak-coupling regime, specifically a two-node system with identical piecewise-linear expanding maps. We derive a necessary and sufficient condition for two facts: the uniqueness of the absolutely continuous invariant measures and the occurrence of intermittent synchronization—i.e., almost every orbit enters and leaves an arbitrarily small neighborhood of the diagonal infinitely often.
Zhang et al. (Wed,) studied this question.