APERIODIC MEAN-FIELD EVOLUTIONS IN COUPLED MAP LATTICES

This paper discusses aperiodic mean-held dynamics in several classes o f coupled map lattices CML's). Two mechanisms underlying complex mean- field evolutions are described. One is the nonlinearity of the mean he ld evolution equation. The other, at play in locally coupled logistic map lattices, is;the presence of ''microscopic'' symmetries. The prese nt work demonstrates that the collective motion in a large class of CM L's is governed by a low-dimensional dynamical system which can, in so me instances, be obtained explicitly. The paper also reports an intere sting kind of mean-field multistability, and discusses the robustness of complex mean-field behaviors under the action of microscopic stocha stic perturbations.