---
_id: '10878'
abstract:
- lang: eng
text: Starting from a microscopic model for a system of neurons evolving in time
which individually follow a stochastic integrate-and-fire type model, we study
a mean-field limit of the system. Our model is described by a system of SDEs with
discontinuous coefficients for the action potential of each neuron and takes into
account the (random) spatial configuration of neurons allowing the interaction
to depend on it. In the limit as the number of particles tends to infinity, we
obtain a nonlinear Fokker-Planck type PDE in two variables, with derivatives only
with respect to one variable and discontinuous coefficients. We also study strong
well-posedness of the system of SDEs and prove the existence and uniqueness of
a weak measure-valued solution to the PDE, obtained as the limit of the laws of
the empirical measures for the system of particles.
acknowledgement: "The second author has been partially supported by INdAM through
the GNAMPA Research\r\nProject (2017) “Sistemi stocastici singolari: buona posizione
e problemi di controllo”. The third\r\nauthor was partly funded by the Austrian
Science Fund (FWF) project F 65."
article_processing_charge: No
article_type: original
author:
- first_name: Franco
full_name: Flandoli, Franco
last_name: Flandoli
- first_name: Enrico
full_name: Priola, Enrico
last_name: Priola
- first_name: Giovanni A
full_name: Zanco, Giovanni A
id: 47491882-F248-11E8-B48F-1D18A9856A87
last_name: Zanco
citation:
ama: Flandoli F, Priola E, Zanco GA. A mean-field model with discontinuous coefficients
for neurons with spatial interaction. Discrete and Continuous Dynamical Systems.
2019;39(6):3037-3067. doi:10.3934/dcds.2019126
apa: Flandoli, F., Priola, E., & Zanco, G. A. (2019). A mean-field model with
discontinuous coefficients for neurons with spatial interaction. Discrete and
Continuous Dynamical Systems. American Institute of Mathematical Sciences.
https://doi.org/10.3934/dcds.2019126
chicago: Flandoli, Franco, Enrico Priola, and Giovanni A Zanco. “A Mean-Field Model
with Discontinuous Coefficients for Neurons with Spatial Interaction.” Discrete
and Continuous Dynamical Systems. American Institute of Mathematical Sciences,
2019. https://doi.org/10.3934/dcds.2019126.
ieee: F. Flandoli, E. Priola, and G. A. Zanco, “A mean-field model with discontinuous
coefficients for neurons with spatial interaction,” Discrete and Continuous
Dynamical Systems, vol. 39, no. 6. American Institute of Mathematical Sciences,
pp. 3037–3067, 2019.
ista: Flandoli F, Priola E, Zanco GA. 2019. A mean-field model with discontinuous
coefficients for neurons with spatial interaction. Discrete and Continuous Dynamical
Systems. 39(6), 3037–3067.
mla: Flandoli, Franco, et al. “A Mean-Field Model with Discontinuous Coefficients
for Neurons with Spatial Interaction.” Discrete and Continuous Dynamical Systems,
vol. 39, no. 6, American Institute of Mathematical Sciences, 2019, pp. 3037–67,
doi:10.3934/dcds.2019126.
short: F. Flandoli, E. Priola, G.A. Zanco, Discrete and Continuous Dynamical Systems
39 (2019) 3037–3067.
date_created: 2022-03-18T12:33:34Z
date_published: 2019-06-01T00:00:00Z
date_updated: 2023-09-08T11:34:45Z
day: '01'
department:
- _id: JaMa
doi: 10.3934/dcds.2019126
external_id:
arxiv:
- '1708.04156'
isi:
- '000459954800003'
intvolume: ' 39'
isi: 1
issue: '6'
keyword:
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1708.04156
month: '06'
oa: 1
oa_version: Preprint
page: 3037-3067
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Discrete and Continuous Dynamical Systems
publication_identifier:
issn:
- 1553-5231
publication_status: published
publisher: American Institute of Mathematical Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: A mean-field model with discontinuous coefficients for neurons with spatial
interaction
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 39
year: '2019'
...