Power law behavior in IF model with random excitatory and inhibitory rates

A new mechanism is proposed to generate power law behavior in interspike interval (ISI) distribution when a collection of neurons group together and fire together. Employing superstatistical framework, the mechanism requires a population of neurons which is characterized by randomly distributed excitatory and inhibitory rates. The distribution of these rates is characterized by independent gamma variates. The effect of randomness in the rates exhibits power law behavior in first passage time of the integrate and fire (IF) model. Extensive Monte Carlo simulation studies of the underlying stochastic differential equation (SDE) are carried out which also depict asymptotically power law behavior for ISI distribution for an ensemble of IF neurons.