Self-organized critical balanced networks: a unified framework

Abstract

Asynchronous irregular (AI) and critical states are two competing frameworks proposed to explain spontaneous neuronal activity. Here, we propose a mean-field model with simple stochastic neurons that generalizes the integrate-and-fire network of Brunel (2000). We show that the point with balanced inhibitory/excitatory synaptic weight ratio $g_c\approx 4$ corresponds to a second order absorbing phase transition usual in self-organized critical (SOC) models. At the synaptic balance point $g_c$, the network exhibits power-law neuronal avalanches with the usual exponents, whereas for nonzero external field the system displays the four usual synchronicity states of balanced networks. We add homeostatic inhibition and firing rate adaption and obtain a self-organized quasi-critical balanced state with avalanches and AI-like activity. Our model might explain why different inhibition levels are obtained in different experimental conditions and for different regions of the brain, since at least two dynamical mechanisms are necessary to obtain a truly balanced state, without which the network may hover in different regions of the presented theoretical phase diagram.

arXiv comment30 pages, 5 figures

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• Role of inhibitory neurons in temporal correlations of critical and supercritical spontaneous activity
• Building a model of the brain: from detailed connectivity maps to network organization
• Critical drift in a neuro-inspired adaptive network
• Physics of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality
• Optimal input reverberation and homeostatic self-organization towards the edge of synchronization