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Conditional mean field for chaotic coupled map lattices

A conditional mean-field approach to strongly chaotic coupled map lattices is presented. It focusses on the time evolution of the one-body probability distribution function p(X) of instantaneous site values. The local environment of a site is modelled in terms of an effective number of independent neighbours, while keeping the Perron-Frobenius operator to account for the action of the local map. This approximation is shown to produce distributions p(X) in agreement with empirical observations of non-trivial collective behaviour, and captures the essence of their dynamics.