We consider a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in
the drift, as a solution of a linear stochastic differential equation driven by a fractional …

The firing behavior and bifurcation of different types of Izhikevich neurons are analyzed
firstly through numerical simulation. Then, a bi-layer neural network driven by random …

High variability in the neuronal response to stimulations and the adaptation phenomenon
cannot be explained by the standard stochastic leaky integrate-and-fire model. The main …

Abstract The Gauss–Diffusion processes are here considered and some relations between
their infinitesimal moments and mean and covariance functions are remarked. The …

We investigate the stochastic processes obtained as the fractional Riemann-Liouville
integral of order α∈(0, 1) of Gauss-Markov processes. The general expressions of the …

A modified LIF-type stochastic model is considered with a non-delta correlated stochastic
process in place of the traditional white noise. Two different mechanisms of reset are …

We find a representation of the integral of the stationary Ornstein–Uhlenbeck (ISOU) process
in terms of Brownian motion B t; moreover, we show that, under certain conditions on the …

Two different stochastic processes are used to model the evolution of the membrane voltage
of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous …

In order to describe neuronal dynamics on different time-scales, we propose a stochastic
model based on two coupled fractional stochastic differential equations, with different …

In order to model the memory and to describe the memory effects in the firing activity of a
single neuron subject to a time-dependent input current, a fractional stochastic Langevin …