Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks

We study in this paper the effect of an 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 non trivial dynamics. This study brings forward a mathematical formalism that allows us to examine the variability of the afterward dynamics according to the parameters of the weight distribution. Provided 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