Spontaneous dynamics of asymmetric random recurrent spiking neural networks

In this letter, we study the effect of a unique initial stimulation on random recurrent networks of leaky integrate-and-fire neurons. Indeed, given a stochastic connectivity, this so-called spontaneous mode exhibits various nontrivial dynamics. This study is based on a mathematical formalism that allows us to examine the variability of the afterward dynamics according to the parameters of the weight distribution. Under the independence hypothesis (e.g., in the case of very large networks), we are able to compute the average number of neurons that fire at a given time-the spiking activity. In accordance with numerical simulations, we prove that this spiking activity reaches a steady state. We characterize this steady state and explore the transients.