Coherent stochastic resonance in the presence of a field

Characteristic effects of stochastic oscillatory forcing on neural firing: analytical theory and comparison to paddlefish electroreceptor data

Stochastic signals with pronounced oscillatory components are frequently encountered in neural systems. Input currents to a neuron in the form of stochastic oscillations could be of exogenous origin, e.g. sensory input or synaptic input from a network rhythm. They shape spike firing statistics in a characteristic way, which we explore theoretically in this report. We consider a perfect integrate-and-fire neuron that is stimulated by a constant base current (to drive regular spontaneous firing), along with Gaussian narrow-band noise (a simple example of stochastic oscillations), and a broadband noise. We derive expressions for the nth-order interval distribution, its variance, and the serial correlation coefficients of the interspike intervals (ISIs) and confirm these analytical results by computer simulations. The theory is then applied to experimental data from electroreceptors of paddlefish, which have two distinct types of internal noisy oscillators, one forcing the other. The theory provides an analytical description of their afferent spiking statistics during spontaneous firing, and replicates a pronounced dependence of ISI serial correlation coefficients on the relative frequency of the driving oscillations, and furthermore allows extraction of certain parameters of the intrinsic oscillators embedded in these electroreceptors.

Survival probability and first-passage-time statistics of a Wiener process driven by an exponential time-dependent drift

The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic process with continuous variables, and important results can be explicitly found from it. The presence of a constant drift does not modify its simplicity; however, when the process has a time-dependent component the analysis becomes difficult. In this work we analyze the statistical properties of the Wiener process with an absorbing boundary, under the effect of an exponential time-dependent drift. Based on the backward Fokker-Planck formalism we set the time-inhomogeneous equation and conditions that rule the diffusion of the corresponding survival probability. We propose as the solution an expansion series in terms of the intensity of the exponential drift, resulting in a set of recurrence equations. We explicitly solve the expansion up to second order and comment on higher-order solutions. The first-passage-time density function arises naturally from the survival probability and preserves the proposed expansion. Explicit results, related properties, and limit behaviors are analyzed and extensively compared to numerical simulations.

Stochastic resonance in one-dimensional diffusion with one reflecting and one absorbing end point

An analysis of the nonmonotonic dependence of the mean-free-passage time on the frequency of a periodic signal [stochastic resonance (SR)] for diffusion on a segment with one absorbing and one reflecting end point shows that SR exists only for some restricted values of parameters. SR always exists if the periodic telegraph signal is replaced by a random one. The latter case is considered in detail.