Random Perturbations of Spiking Activity in a Pair of Coupled Neurons
Boris Gutkin , Juergen Jost and Henry C. Tuckwell
We examine the behavior of two excitation coupled neurons forced by uncorrelated noise. We find that the underlying bifurcation structure of spike generation explains the different mechanisms that lead to synaptically sustained firing (the up state) in the different types of neurons and the effect of random noise on the stability of the up-state. Hodgkin-Huxley model neurons with standard parameters, which are Type 2, need to be in the bistable regime, in order for synaptic transmission to initiate joint spiking. In this case further synaptic transmission is not necessary to sustain the up state. In Type 1 cells (models), typified by a quadratic integrate and fire model, synaptic coupling can initiate oscillatory behavior and is needed to sustain it. In both cases Gaussian white noise can again terminate it. We locally determine an approximate basin of attraction, A, of the periodic orbit and explain the firing behaviour in terms of the effects of noise on the probability of escape of trajectories from A.