Neural networks and interacting point processes

Abstract

Event Abstract Back to Event Neural networks and interacting point processes Stefano Cardanobile1* and Stefan Rotter1 1 Albert-Ludwigs-University, Germany Inhomogeneous Poisson processes are much employed for modelling and analyzing neuronal spike data; the basic parameter of such models is the instantaneous firing rate. Here, we investigate networks of coupled point processes that use the instantaneous firing rates of their neurons as state variables. Generalizing Hawkes (1971a, 1971b) linear model, our nonlinear description also admits inhibitory interactions. In particular, we present: (1) a mathematical model of interacting point processes where spikes trigger changes in the instantaneous firing rates of the postsynaptic neurons; (2) differential equations for mean and variance of the firing rates; (3) a point process equivalent of the leaky integrate-and-fire neuron.