CONDITIONAL MEAN-FIELD FOR CHAOTIC COUPLED MAP LATTICES

A conditional mean-field approach to strongly chaotic coupled map latt ices is presented. Tt focusses on the time evolution of the one-body p robability distribution function p(X) of instantaneous site values. Th e local environment of a site is modelled in terms of an effective num ber of independent neighbours, while keeping the Perron-Frobenius oper ator to account for the action of the local map. This approximation is shown to produce distributions p(X) in agreement with empirical obser vations of non-trivial collective behaviour, and captures the essence of their dynamics.