Multi-class oscillating systems of interacting neurons

Autor(es)

Ditlevsen, Susanne ; Locherbach, Eva

• Tipo de documento: Artigo Científico
• Fonte: Stochastic Processes and their Applications; v. 127, n. 6, p. 1840-1869, JUN 2017.
• Citações Web of Science: 10

Resumo

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)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Jefferson Antonio Galves
• Linha de fomento: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs