UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

On a Finite-Size Neuronal Population Equation

Schmutz, Valentin; Löcherbach, Eva; Schwalger, Tilo; (2023) On a Finite-Size Neuronal Population Equation. SIAM Journal on Applied Dynamical Systems , 22 (2) pp. 996-1029. 10.1137/21m1445041. Green open access

[thumbnail of schmutz-et-al-2023-on-a-finite-size-neuronal-population-equation.pdf]
Preview
PDF
schmutz-et-al-2023-on-a-finite-size-neuronal-population-equation.pdf - Published Version

Download (3MB) | Preview

Abstract

Population equations for infinitely large networks of spiking neurons have a long tradition in theoretical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear stochastic integral equation. We prove that, in the case of leaky integrate-and-fire neurons with escape noise and for a slightly simplified version of the model, the equation is well-posed and stable in the sense of Brémaud and Massoulié. The proof combines methods from Markov processes taking values in the space of positive measures and nonlinear Hawkes processes. For applications, we also provide efficient simulation algorithms.

Type: Article
Title: On a Finite-Size Neuronal Population Equation
Open access status: An open access version is available from UCL Discovery
DOI: 10.1137/21m1445041
Publisher version: https://doi.org/10.1137/21m1445041
Language: English
Additional information: © 2023 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license. This work is licensed under a Creative Commons Attribution 4.0 International License.
Keywords: stability, finite-size fluctuations, nonlinear Hawkes processes, piecewise deterministic Markov processes, Meyn--Tweedie theory, spiking neuron, SPDEs driven by Poisson random measure
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Brain Sciences > UCL Queen Square Institute of Neurology > Imaging Neuroscience
URI: https://discovery.ucl.ac.uk/id/eprint/10178709
Downloads since deposit
8Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item