MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Random perturbations of spiking activity in a pair of coupled neurons

Boris Gutkin, Jürgen Jost and Henry Tuckwell


We examine the effects of stochastic input currents on the firing behaviour of two coupled Type 1 or Type 2 neurons. In Hodgkin-Huxley model neurons with standard parameters, which are Type 2, in the bistable regime, synaptic transmission can initiate oscillatory joint spiking, but white noise can terminate it. In Type 1 cells (models), typified by a quadratic integrate and fire model, synaptic coupling can cause oscillatory behaviour in excitatory cells, but Gaussian white noise can again terminate it. We locally determine an approximate basin of attraction, ${\cal A}$, of the periodic orbit and explain the firing behaviour in terms of the effects of noise on the probability of escape of trajectories from ${\cal A}$.


Related publications

2008 Journal Open Access
Henry C. Tuckwell, Jürgen Jost and Boris Gutkin

Random perturbations of spiking activity in a pair of coupled neurons

In: Theory in biosciences, 127 (2008) 2, pp. 135-139