Fractional Ornstein-Uhlenbeck process with stochastic forcing, and its applications
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 drift, as a solution of a linear stochastic differential equation driven by a fractional …
[HTML][HTML] Spatiotemporal patterns and collective dynamics of bi-layer coupled Izhikevich neural networks with multi-area channels
G Wang, Y Fu - Mathematical Biosciences and Engineering, 2023 - aimspress.com
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 …
firstly through numerical simulation. Then, a bi-layer neural network driven by random …
Colored noise and a stochastic fractional model for correlated inputs and adaptation in neuronal firing
E Pirozzi - Biological cybernetics, 2018 - Springer
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 …
cannot be explained by the standard stochastic leaky integrate-and-fire model. The main …
Closed-form solutions for the first-passage-time problem and neuronal modeling
A Buonocore, L Caputo, G D'Onofrio, E Pirozzi - Ricerche di Matematica, 2015 - Springer
Abstract The Gauss–Diffusion processes are here considered and some relations between
their infinitesimal moments and mean and covariance functions are remarked. The …
their infinitesimal moments and mean and covariance functions are remarked. The …
Fractionally integrated Gauss-Markov processes and applications
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 …
integral of order α∈(0, 1) of Gauss-Markov processes. The general expressions of the …
[PDF][PDF] On a stochastic neuronal model integrating correlated inputs
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 …
process in place of the traditional white noise. Two different mechanisms of reset are …
Integrated stationary Ornstein–Uhlenbeck process, and double integral processes
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 …
in terms of Brownian motion B t; moreover, we show that, under certain conditions on the …
[PDF][PDF] Successive spike times predicted by a stochastic neuronal model with a variable input signal
G D'Onofrio, E Pirozzi - Mathematical Biosciences and Engineering, 2016 - iris.unito.it
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 …
of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous …
Some Fractional Stochastic Models for Neuronal Activity with Different Time-Scales and Correlated Inputs
E Pirozzi - Fractal and Fractional, 2024 - mdpi.com
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 …
model based on two coupled fractional stochastic differential equations, with different …
On fractional stochastic modeling of neuronal activity including memory effects
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 …
single neuron subject to a time-dependent input current, a fractional stochastic Langevin …