Neuronal Dynamics: from Complexity to Simplicity

Abstract

An analytical study is performed to obtain the phase description of a network of Leaky Integrate-and-Fire (LIF) neurons. We start by discussing the behaviour of single LIF neuron in the presence of a constant current and then derive the corresponding phase oscillator model for some parameters setup. In the case of two identical LIF neurons where the interactions are ruled by the weak pulse input, we determine the analytical expression for the phase response curve. Next, we extend the phase reduction principles to a generic case of N networks of identical LIF neurons. The final model of so-called phase oscillators is widely used to study synchronization in many natural systems. Through numerical simulations, we find an agreement between the LIF neurons and the phase oscillators model.