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.
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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 |
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