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(-beta), with an exponent beta close to 1 (pink noise). This exponent is predicted to be connected with the exponent gamma related to the scaling of the average size with the duration of avalanches of activity. "Mean field" models of neural dynamics predict exponents beta and gamma 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 beta and gamma markedly different from those of mean field, respectively around 1 and 1.3. The exponents alpha and tau 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.