Stability of Antiphase Oscillations in a Network of Inhibitory Neurons

作者：Lee E^*; Terman D

来源：SIAM Journal on Applied Dynamical Systems, 2015, 14(1): 448-480.

DOI：10.1137/140991236

• neuronal network
• relaxation oscillator
• inhibitory synapses
• antiphase solution

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.

• 出版日期2015