Multi-class oscillating systems of interacting neurons

Ditlevsen, Susanne; Locherbach, Eva

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Multi-class oscillating systems of interacting neurons

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Author(s):	Ditlevsen, Susanne ; Locherbach, Eva Total Authors: 2
Document type:	Journal article
Source:	Stochastic Processes and their Applications; v. 127, n. 6, p. 1840-1869, JUN 2017.
Web of Science Citations:	10
Abstract
We consider multi-class systems of interacting nonlinear Hawkes processes modeling several large families of neurons and study their mean field limits. As the total number of neurons goes to infinity we prove that the evolution within each class can be described by a nonlinear limit differential equation driven by a Poisson random measure, and state associated central limit theorems. We study situations in which the limit system exhibits oscillatory behavior, and relate the results to certain piecewise deterministic Markov processes and their diffusion approximations. (C) 2016 The Author(s). Published by Elsevier B.V. (AU)

FAPESP's process:	13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat
Grantee:	Oswaldo Baffa Filho
Support Opportunities:	Research Grants - Research, Innovation and Dissemination Centers - RIDC

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