Average firing rate of a neural network with dynamical disorder

Abstract

We analyse the effects of time-varying synaptic background activity on the steady-state firing rate of a compartmental model neural network with shunting. The background is taken to be a multi-component dichotomous coloured noise process distributed randomly across the compartments of each neuron. We exploit the formal similarity between the neural network model and a model of excitons moving on a lattice with random modulations of the local energy at each site. In particular, we use a dynamical coherent potential approximation and the method of partial cumulants to evaluate the single-neuron Green's function averaged over the stochastic background. This is then used to determine the firing rate. It is found that the firing rate increases with the variance and correlation time of the coloured noise process.