Dynamics of Stochastic Integrate-and-Fire Networks

The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual neurons, while biological neurons are highly complex cells. The hallmark neuronal nonlinearity is the action potential, a stereotyped pulse leading to neuron transmitter release and finishes with the neuron’s membrane potential at an approximately constant reset value. Here, we develop a statistical field theory for networks of stochastic spiking neurons. We use this to investigate the mean field dynamics of the population activity and the impact of nonlinear spike emission and nonlinear spike resets on the population activity, and compare the roles of inhibitory interactions and single-neuron spike resets in stabilizing neural network activity.