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We show that under certain simple assumptions on the topology (structure) ofnetworks of strongly interacting chaotic elements a phenomenon of long rangeaction takes place, namely that the asymptotic (as time goes to infinity)dynamics of an arbitrary large network is completely determined by its boundaryconditions. This phenomenon takes place under very mild and robust assumptionson local dynamics with short range interactions. However, we show that it isunstable with respect to arbitrarily weak local random perturbations.Comment: 15 page

Long range action in networks of chaotic elements