The Properties and Stability Analysis of an Integrate-and-Fire Model

In this paper, a simplified integrate-and-fire (IF) neural network is introduced. This network possesses lateral interactions of the shunting inhibitory type only; hence, it is also called shunting inhibitory cellular neural network. Its derivation and biophysical interpretation are presented in this article, along with a stability analysis of its dynamics. In particular, it is shown that the IF model is bounded input bounded output stable dynamical system. Two indices of firing variability are evaluated, which are the ratio of the variance to the mean for the number of action potentials evoked by a constant and a random stimulus respectively, and the rate coefficient of variation of the interspike interval (ISI) distribution (standard deviation / mean ISI).