Stability of Antiphase Oscillations in a Network of Inhibitory Neurons

Abstract

We investigate antiphase, oscillatory behavior in a model network of two mutually coupled, identical neurons with inhibitory synapses. Each neuron is described as a relaxation oscillator, and the synapses are modeled in such a way that the synaptic activation occurs rapidly, but its inactivation proceeds with a speed comparable to the slow process of the intrinsic oscillator. Using fast/slow analysis, we construct a two-dimensional map, reducing the problem of proving the existence of a stable antiphase solution of the model into proving the existence of a stable fixed point of the map. Through a detailed analysis of this map, we derive precise conditions on the network parametersparticularly, the decay rate of the synapses and duty cycle of the oscillator-for when there exists a stable antiphase solution.