SELF-ORGANIZATION OF INTERACTING POLYA URNS

We introduce a simple model which shows non-trivial self organized cri tical properties. The model describes a system of interacting units, m odelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations - stochastic, quenched and deterministic - are shown to reproduce the same dynamics. Among the no vel features of the model are a non-homogeneous stationary state, the presence of a non-stationary critical phase and non-trivial exponents even in mean field. We discuss simple interpretations in term of biolo gical evolution and earthquake dynamics and we report on extensive num erical simulations in dimensions d = 1, 2 as well as in the random nei ghbors limit.