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

Transient termination of synaptically sustained spiking by stochastic inputs in a pair of coupled Type 1 neurons

Boris Gutkin, Jürgen Jost and Henry Tuckwell


We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling can cause sustained firing of oscillatory behavior which is necessarily antiphase. Additive Gaussian white noise can transiently terminate the oscillations, hence destroying the stable limit cycle. Further application of the noise may return the system to spiking activity. In a particular noise range, the transition times between the oscillating and the resting state are strongly asymmetric. We numerically investigate an approximate basin of attraction, $\mathcal{A}$, of the periodic orbit and use Markov process theory to explain the firing behavior in terms of the probability of escape of trajectories from $\mathcal{A}$.

05.40.Ca, 87.10.+e, 87.16.Ac, 87.18.Sn, 87.19.La

Related publications

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

Transient termination of spiking by noise in coupled neurons

In: epl, 81 (2008) 2, p. 20005