Stochastic resonance in a sinusoidally forced LIF model with noisy threshold

First-passage times in integrate-and-fire neurons with stochastic thresholds

We consider a leaky integrate-and-fire neuron with deterministic subthreshold dynamics and a firing threshold that evolves as an Ornstein-Uhlenbeck process. The formulation of this minimal model is motivated by the experimentally observed widespread variation of neural firing thresholds. We show numerically that the mean first-passage time can depend nonmonotonically on the noise amplitude. For sufficiently large values of the correlation time of the stochastic threshold the mean first-passage time is maximal for nonvanishing noise. We provide an explanation for this effect by analytically transforming the original model into a first-passage-time problem for Brownian motion. This transformation also allows for a perturbative calculation of the first-passage-time histograms. In turn this provides quantitative insights into the mechanisms that lead to the nonmonotonic behavior of the mean first-passage time. The perturbation expansion is in excellent agreement with direct numerical simulations. The approach developed here can be applied to any deterministic subthreshold dynamics and any Gauss-Markov processes for the firing threshold. This opens up the possibility to incorporate biophysically detailed components into the subthreshold dynamics, rendering our approach a powerful framework that sits between traditional integrate-and-fire models and complex mechanistic descriptions of neural dynamics.

Stochastic resonance in two simple compare-and-fire models

Two neural models are analysed and shown to exhibit the stochastic resonance effect. Namely, they respond to an underthreshold sinusoidal signal with an output signal whose signal-to-noise ratio (SNR) firstly increases then decreases as the intensity of noise affecting the system increases. The resonance curves are determined, analytically for the first and simplest model and by a synthetic method for the second one, and the respective resonant behaviours are illustrated and interpreted.

Stochastic resonance in the LIF models with input or threshold noise

In this paper, two stochastic versions of the LIF neural model are considered: one with the noise signal applied to the firing threshold, the other having it added to the input current. Then, adopting a discontinuous stepwise noise whose innovations are uncorrelated and gaussian distributed, the behaviours of the two models pertaining to the stochastic resonance (SR) are analysed and compared. Furthermore, it is shown that introducing a suitable time correlation into the noise signal brings us from the first model to the second one.