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
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.
PACS: 64.60.Ht – Dynamic critical phenomena / 64.60.Lx – Self-organized criticality; avalanche effect
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998