Edge of chaos and scale-free avalanches in neural networks with heavy-tailed synaptic disorder

Different scenarios of the transition to chaos in randomly connected neural networks were extensively studied over the last 30 years. According to the prevailing assumption rooted in the central limit theorem, the total synaptic input current of each neuron can be modeled as a Gaussian random variable (Gaussian assumption). Here we argue that the Gaussian assumption cannot account for some of the experimentally observed features of neuronal circuits. We propose a novel, analytically tractable connectivity model with power-law distributed synaptic weights. When threshold neurons with biologically plausible many inputs are considered, our model, in contrast to the Gaussian counterpart, features a continuous transition to chaos and can reproduce biologically relevant low activity levels and associated scale-free avalanches, i.e. bursts of activity with power-law distributions of sizes and lifetimes.