For the study of the behavior of noisy neuronal models, Rodriguez and Tuckwell have
introduced an elegant and systematic method which consists of replacing the system of …

A master-equation approach to the stochastic neurodynamics proposed by Cowan [in
Advances in Neural Information Processing Systems 3, edited by RP Lippman, JE Moody …

Dynamical stochastic models of single neurons and neural networks often take the form of a
system of n≥ 2 coupled stochastic differential equations. We consider such systems under …

We present for the first time an analytical approach for determining the time of firing of
multicomponent nonlinear stochastic neuronal models. We apply the theory of first exit times …

We discuss the statistics of spikes trains for different types of integrate-and-fire neurons and
different types of synaptic noise models. In contrast with the usual approaches in …

Neural dynamics is often investigated with tools from bifurcation theory. However, many
neuron models are stochastic, mimicking fluctuations in the input from unknown parts of the …

An analytical approach is presented for determining the response of a neuron or of the
activity in a network of connected neurons, represented by systems of nonlinear ordinary …

We study the stochastic FitzHugh–Nagumo equations, modelling the dynamics of neuronal
action potentials in parameter regimes characterized by mixed-mode oscillations. The …

We study excitability phenomena for the stochastically forced FitzHugh-Nagumo system
modeling a neural activity. Noise-induced changes in the dynamics of this model can be …

The variability and mean of the firing rate of Hodgkin-Huxley and FitzHugh-Nagumo neurons
subjected to random synaptic input are only weakly dependent on the level of inhibitory …