Related Experiment Video
Updated: Jun 10, 2026

Real-time Electrophysiology: Using Closed-loop Protocols to Probe Neuronal Dynamics and Beyond
Published on: June 24, 2015
A discrete time neural network model with spiking neurons: II: dynamics with noise
1Equipe systèmes dynamiques, interactions en physique, biologie, chimie, Laboratoire Jean-Alexandre Dieudonné, Université de Nice, Parc Valrose, 06000 Nice, France. bruno.cessac@inria.fr
Abstract:
We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.
Related Concept Videos
The Role of Ion Channels in Neuronal Computation
Sometimes a single EPSP is strong enough to induce an action potential in the postsynaptic neuron. However, multiple presynaptic inputs must often create EPSPs around the same time for the postsynaptic neuron to be sufficiently depolarized to fire an action potential.
Modeling with Differential Equations
Neural Circuits
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Classification of Systems-II
Neurons: The Axon
The axon attaches to the cell body at a cone-shaped elevation called the axon hillock. The initial part of the axon, closest to the hillock, is known as the initial segment.
Propagation of Action Potentials
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
