Bifurcations in a synaptically coupled Morris-Lecar neuron model

We study bifurcations arising in a system of two synaptically interconnected neurons where the individual neurons are represented by the Morris-Lecar model. The synaptic interconnection strength and externally applied input dc current are treated as bifurcation parameters and the critical values that result in neural excitability are identified. It is seen that the synaptic coupling strength, (i) strongly reduces the threshold of external current that determines excitability in isolated neurons and (ii) preserves the type I mechanism of neural excitability. As an interesting consequence, individual neurons which are at rest for a given set of parameters can be rendered excitable under synaptic interconnection. Numerical simulations are presented to verify the analytical results.