Eur. Phys. J. B 3, 417-420 (1998)
https://doi.org/10.1007/s100510050330

Self organization of interacting polya urns

¹ International School for Advanced Studies (SISSA) and INFM unit, V. Beirut 2-4, 34014, Trieste, Italy
² Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Str. 38, 01187 Dresden, Germany

Corresponding author: ^a marsili@sissa.it

Received: 18 February 1998
Revised: 20 March 1998
Accepted: 29 March 1998
Published online: 15 June 1998

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.