Self-organization without conservation: are neuronal avalanches generically critical?

Abstract

Recent experiments on cortical neural networks have revealed the existence of well-definedavalanches of electrical activity. Such avalanches have been claimed to be generically scaleinvariant—i.e. power law distributed—with many exciting implications in neuroscience.Recently, a self-organized model has been proposed by Levina, Herrmann and Geisel toexplain this empirical finding. Given that (i) neural dynamics is dissipative and (ii) there isa loading mechanism progressively ‘charging’ the background synaptic strength, thismodel/dynamics is very similar in spirit to forest-fire and earthquake models, archetypicalexamples of non-conserving self-organization, which have recently been shown to lack truecriticality. Here we show that cortical neural networks obeying (i) and (ii) are notgenerically critical; unless parameters are fine-tuned, their dynamics is eithersubcritical or supercritical, even if the pseudo-critical region is relatively broad.This conclusion seems to be in agreement with the most recent experimentalobservations. The main implication of our work is that, if future experimental research oncortical networks were to support the observation that truly critical avalanchesare the norm and not the exception, then one should look for more elaborate(adaptive/evolutionary) explanations, beyond simple self-organization, to account for this.