A dynamical model of a binary neural network is developed which incorporates certain
important neurophysiological features of real neurons missing from most artificial network …

Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the
current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire …

The spontaneous firing activity of single neurons can be viewed in the framework of
stochastic modelling. Of special interest in this regard is the point process defined by the …

Considerable attention has been paid in the literature to the development of biologically
interpretable mathematical models of spontaneous stationary neuronal spike-train activity …

Reduced models have long been used as a tool for the analysis of the complex activity
taking place in neurons and their coupled networks. Recent advances in experimental and …

Abstract The Ornstein-Uhlenbeck process has been proposed as a model for the
spontaneous activity of a neuron. In this model, the firing of the neuron corresponds to the …

Model neural networks are built of model neurons. While real biological neurons exhibit
extremely complex and rich behavior, neuronal dynamics must be considerably simplified to …

Mathematical modeling and simulation of dynamic biochemical systems are receiving
considerable attention due to the increasing availability of experimental knowledge of …

We consider applications of path-integral methods to the analysis of a stochastic hybrid
model representing a network of synaptically coupled spiking neuronal populations. The …

The leaky integrate-and-fire neuronal model proposed in Stevens and Zador, in which time
constant and resting potential are postulated to be time dependent, is revisited within a …