Modeling neuronal avalanches and long-range temporal correlations at the emergence of collective oscillations: continuously varying exponents mimic M/EEG results

Abstract

We revisit the CROS (\"CRitical OScillations\") model which was recently proposed as an attempt to reproduce both scale-invariant neuronal avalanches and long-range time correlations. With excitatory and inhibitory stochastic neurons locally connected in a two-dimensional disordered network, the model exhibits a transition from an active to an oscillating state. Precisely at the transition, the fluctuations of the network activity have detrended fluctuation analysis (DFA) exponents close to one, and avalanches (defined as supra-threshold activity) have power law distributions of size and duration. By simulating larger system sizes, we show that, differently from previous results, the exponents governing the distributions of avalanche size and duration are not necessarily those of the mean-field directed percolation universality class (3/2 and 2, respectively). Instead, exponents obtained via a maximum-likelihood estimator vary continuously in a narrow region of parameter space. Around that critical region, moreover, the values of avalanche and DFA exponents display a spread with negative correlations, in qualitative agreement with the interindividual variability that was experimentally observed in M/EEG data.