Network activity in a Morris–Lecar population density model

Abstract

A population density approach is presented to simulate the network activity of Morris–Lecar (ML) neurons. The network is composed of identical excitatory and inhibitory ML neurons. Each neuron randomly receives excitatory and inhibitory connections from other neurons in the network and an excitatory external input which is described by an independent Poisson process from neurons outside the network. We solve the evolution equation for the population density approach numerically. The results were compared against conventional computation for groups of individual neurons in a few example networks. We found that when the neuronal network comprises a large number of identical excitatory ML neurons that are sparsely connected, the population density approach gives a closer approximation to the network activity. We also demonstrated that the population density approach using the ML neuron model can be used to simulate the activities of type I and type II neurons (integrators and resonators) in a network of sparsely connected inhibitory and excitatory neurons that was not possible using the integrate-and-fire neuron model.