Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh

Clarification and Complement to “Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons”

Published:2015-09-01 Issue:1 Volume:5 Page:
ISSN:2190-8567
Container-title:The Journal of Mathematical Neuroscience (JMN)
language:en
Short-container-title:J. Math. Neurosc.

Author:

Bossy Mireille,Faugeras Olivier,Talay Denis

Publisher

Springer Science and Business Media LLC

Subject

Neuroscience (miscellaneous)

Link

http://link.springer.com/content/pdf/10.1186/s13408-015-0031-8.pdf

Reference11 articles.

1. Baladron J, Fasoli D, Faugeras O, Touboul J. Mean field description and propagation of chaos in networks of Hodgkin–Huxley and FitzHugh–Nagumo neurons. J Math Neurosci 2012, 2:10.

2. Lecture notes in mathematics;AS Sznitman,1989

3. McKean HP. Propagation of chaos for a class of non-linear parabolic equations. In: 1967 stochastic differential equations (Lecture series in differential equations, session 7, Catholic Univ.). Arlington: Air Force Office Sci. Res.; 1967. p. 41–57.

4. Scheutzow M. Uniqueness and nonuniqueness of solutions of Vlasov–McKean equations. J Aust Math Soc A. 1987;43(2):246–56.

5. Touboul J. The propagation of chaos in neural fields. Ann Appl Probab. 2014;24(3):1298–328.

Cited by 43 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Strong convergence of Euler–Maruyama schemes for doubly perturbed McKean–Vlasov stochastic differential equations;Communications in Nonlinear Science and Numerical Simulation;2024-05

2. An explicit Milstein-type scheme for interacting particle systems and McKean–Vlasov SDEs with common noise and non-differentiable drift coefficients;The Annals of Applied Probability;2024-04-01

3. Particle method and quantization-based schemes for the simulation of the McKean-Vlasov equation;ESAIM: Mathematical Modelling and Numerical Analysis;2024-03

4. EEG generation mechanism of lower limb active movement intention and its virtual reality induction enhancement: a preliminary study;Frontiers in Neuroscience;2024-01-30

5. Wasserstein contraction for the stochastic Morris-Lecar neuron model;Kinetic and Related Models;2024