Criticality of a dissipative self-organizing process in a dynamic population

2006/04/24 by Juanico, D. E., Monterola, C., Saloma, C.
#Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences

paper · doi:10.48550/arxiv.nlin/0604058

Abstract

We derive a general formulation of the self-organized branching process by considering sandpile dynamics in an evolving population characterized by "birth" (excitation) and "death" (de-excitation) of active sites (z=1). New active sites are born in empty sites (z=0) with a probability of η, whereas active sites die, thus becoming empty, with a probability λ. Subsequently, when an active site becomes unstable (z=2), it topples by transferring two grains to two randomly chosen sites with probability α or, by transferring only one grain to a randomly selected site (while retaining the other) with probability β=1+\fracλη-2α, thus remaining active after toppling. We show that when sandpile dynamics occurs in an evolving population, self-organized criticality, characterized by a power-law avalanche size distribution with exponent τ_s=3/2 and power-law avalanche duration distribution with exponent τ_T=2 at very high dimension n >> 1, is achieved even in the presence of dissipation (ε= 1-α- β> 0), contrary to previous claims.

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