Power spectrum and critical exponents in the 2D stochastic Wilson–Cowan model

The power spectrum of brain activity is composed by peaks at characteristic frequencies superimposed to a background that decays as a power law of the frequency, f-β, with an exponent β close to 1 (pink noise). This exponent is predicted to be connected with the exponent γ related to the scaling of the average size with the duration of avalanches of activity. “Mean field” models of neural dynamics predict exponents β and γ equal or near 2 at criticality (brown noise), including the simple branching model and the fully-connected stochastic Wilson–Cowan model. We here show that a 2D version of the stochastic Wilson–Cowan model, where neuron connections decay exponentially with the distance, is characterized by exponents β and γ markedly different from those of mean field, respectively around 1 and 1.3. The exponents α and τ of avalanche size and duration distributions, equal to 1.5 and 2 in mean field, decrease respectively to 1.29 ± 0.01 and 1.37 ± 0.01. This seems to suggest the possibility of a different universality class for the model in finite dimension.