Dissipative self-organized branching in a dynamic population

Abstract

We study a locally nonconservative self-organized branching process (SOBP) in an open system of excitable agents exhibiting spontaneous excitation and deexcitation. The SOBP achieves criticality even in the absence of energy conservation as the population relaxes to a stable state with no overexcited agent. Criticality is widely thought to happen only in a locally conservative SOBP. Our model explains the observed characteristic size in the size distribution of tuna fish schools and the neuronal avalanches in cortical networks.

Being Critical of Criticality in the Brain

“…Critio: It is still an open question as to how the network operates at the critical point, if it is indeed operating a critical point, and there have been several interesting proposals and experiments related to this topic (Bienenstock, 1995; Chialvo and Bak, 1999; de Carvalho and Prado, 2000; Bak and Chialvo, 2001; Eurich et al, 2002; Freeman, 2005; Kozma et al, 2005; de Arcangelis et al, 2006; Hsu and Beggs, 2006; Abbott and Rohrkemper, 2007; Buice and Cowan, 2007, 2009; Juanico et al, 2007; Levina et al, 2007, 2009; Pellegrini et al, 2007; Hsu et al, 2008; Stewart and Plenz, 2008; Allegrini et al, 2009; Magnasco et al, 2009; Tanaka et al, 2009; Buice et al, 2010; de Arcangelis and Herrmann, 2010; Kello and Mayberry, 2010; Millman et al, 2010; Tetzlaff et al, 2010; Rubinov et al, 2011; Droste et al, 2012). Whether the network gets to criticality through self-organization or not, it does seem that at least some networks of neurons can operate at the critical point.…”

An open hypothesis: Is epilepsy learned, and can it be unlearned?

“…Although not identical to the critical point of phase transitions, because it lacks the property of universality, the critical point of neural systems has attracted increasing theoretical and computational interest because of its importance to neural systems function [21,[30][31][32][33][34][35][36][37][38][39][40]. A critical neural system is balanced between a phase where activity is damped and a phase where activity is expanding.…”

Avalanche statistics of driven granular slides in a miniature mound

“…One class of models, based on self‐organized criticality (SOC) [ Hergarten and Neugebauer , 1998; Piegari et al , 2006], hint at some possible mechanisms yielding the observed statistics. SOC is a theory underlying the spontaneous emergence of critical‐like behavior (i.e., power laws and critical exponents) in systems for which the timescales between buildup and release of stress are separated, and for which the stress‐transfer mechanism is generally nonconservative [ Juanico et al , 2007a, 2007b; Juanico and Monterola , 2007]. SOC concepts have aroused great interest in the study of granular matter [ Jaeger et al , 1989], a well‐known example of which is the ricepile experiment [ Frette et al , 1996].…”