Stable Synchronized Periodic Solutions in a Pair of Mutually Inhibitory Model Neurons with Conduction Delays

초록

We investigate the synchronizing properties of two synaptically coupled model neurons in the presence of conduction delays. The neurons are modeled as relaxation oscillators, and they interact through inhibitory synapses that activate rapidly but decay slowly. We derive a reduced system through a slow/fast decomposition process, and special coordinates are introduced into the system. Then we construct a map, for which a stable fixed point corresponds to a stable synchronized periodic (SP) solution. The functional benefit of these coordinates is that, on the stability of an SP solution, the map can be decomposed into one-dimensional submaps. By analyzing these submaps, we examine how conduction delays affect the stability of the SP solution, depending on the period and duty cycle of an intrinsic oscillator and the synaptic decay rate.

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