Oscillatory Rhythms in a Model Network of Excitatory and Inhibitory Neurons

Oscillatory rhythms are investigated in a model network where a pair of excitatory neurons interact via an inhibitory neuron. Each individual neuron is modeled as a relaxation oscillator, and a slow/fast decomposition process reduces the problem of a stable oscillatory rhythm to the problem of a stable fixed point of a map. Further reduction of the map is made by finding an invariant manifold. A detailed analysis of the reduced map reveals how different types of stable oscillatory rhythms arise, depending on the intrinsic properties of the individual neurons and the synaptic time constant.