Dynamics of synaptically coupled FitzHugh-Nagumo neurons

An extended FitzHugh-Nagumo model is developed to model the synaptic coupling of neurons and the associated dynamics. The neurons are coupled via chemical synapses, which can excite or inhibit the postsynaptic neuron. The neurotransmitter-receptor dynamics is governed with a gating dynamic, which allows for the distinction between fast and slow synapses. Detailed nonlinear dynamics analysis are performed for simple neural motifs of a self-synapsed neuron and two synaptically coupled neurons for the instabilities that lead to neural oscillations, and the associated phase diagrams are obtained. Interesting dynamics such as synchronization of fast and slow firing neurons, frequency enhancement, quiescent neurons coupled to oscillators, chaotic spiking, and periodic bursting are found.