The integrate-and-fire neuron model is one of the most widely used models for analyzing the
behavior of neural systems. It describes the membrane potential of a neuron in terms of the …

The cortex is a complex system, characterized by its dynamics and architecture, which
underlie many functions such as action, perception, learning, language, and cognition. Its …

The activity of neurons in the brain is noisy in that their firing times are random when they
are firing at a given mean rate. This introduces a random or stochastic property into brain …

Mathematical models are an important tool for neuroscientists. During the last 30 years
many papers have appeared on single neuron description and specifically on stochastic …

Parameters in diffusion neuronal models are divided into two groups; intrinsic and input
parameters. Intrinsic parameters are related to the properties of the neuronal membrane and …

The response of a noisy integrate-and-fire neuron with reset to periodic input is investigated.
We numerically obtain the first-passage-time density of the pertaining Ornstein-Uhlenbeck …

We provide a comparative analysis of qualitative features of different numerical methods for
the inhomogeneous geometric Brownian motion (IGBM). The limit distribution of the IGBM …

The stochastic Ornstein-Uhlenbeck neuronal model is studied, and estimators of the model
input parameters, depending on the firing regime of the process, are derived. Closed …

Synaptic noise due to intense network activity can have a significant impact on the
electrophysiological properties of individual neurons. This is the case for the cerebral cortex …

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical
tractability. They have been widely applied to gain understanding of the underlying …