Burst distributions in stochastic rate model of neuronal populations

Abstract

Neuronal avalanches have been proposed as a new dynamical behavior present in the isolated neocortex. This suggests a critical state in the brain where information transmission is optimized. Here we analyze the emergence of avalanches in the stochastic rate model introduced by Benayoun et al. (2010), in which random bursting occurs with balanced excitation and inhibition at large enough values of the total synaptic strength, wₛ = w+w'. We investigate the transition from Poisson firing at low synaptic strength to power-law bursting by following the parameters of a dual power-law fit. Results show that neuronal spikes start to deviate from the Poissonian shape from wₛ ≈ 1 into an exponential distribution before completely obeying a power-law distribution for wₛ ≥ 14. The results provide better insight on the behavior of neuronal populations with respect to total synaptic strength, which is a variable that can be controlled experimentally.