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Self Organization of Interacting Polya Urns

Matteo Marsili·Angelo Valleriani
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Abstract

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled 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 novel 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 biological evolution and earthquake dynamics and we report on extensive numerical simulations in dimensions $d=1,2$ as well as in the random neighbors limit.

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Matteo Marsili, Angelo Valleriani. 1998-02-16. Self Organization of Interacting Polya Urns. https://doi.org/10.1007/s100510050330

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