Hydrodynamic Limit for Interacting Neurons

Autor(es)

De Masi, A. ^[1] ; Galves, A. ^[2] ; Loecherbach, E. ^[3] ; Presutti, E. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Aquila, I-67100 Laquila - Italy

^[2] Univ Sao Paulo, Sao Paulo - Brazil

^[3] Univ Cergy Pontoise, Cergy Pontoise - France

^[4] GSSI, Laquila - Italy

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 158, n. 4, p. 866-902, FEB 2015.
• Citações Web of Science: 27

Resumo

This paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical and by electrical synapses. This system can be informally described as follows. Each neuron spikes randomly following a point process with rate depending on its membrane potential. At its spiking time, the membrane potential of the spiking neuron is reset to the value 0 and, simultaneously, the membrane potentials of the other neurons are increased by an amount of potential 1/N. This mimics the effect of chemical synapses. Additionally, the effect of electrical synapses is represented by a deterministic drift of all the membrane potentials towards the average value of the system. We show that, as the system size N diverges, the distribution of membrane potentials becomes deterministic and is described by a limit density which obeys a non linear PDE which is a conservation law of hyperbolic type. (AU)

• Processo FAPESP: 13/07699-0 - Centro de Pesquisa, Inovação e Difusão em Neuromatemática - NeuroMat
• Beneficiário: Oswaldo Baffa Filho
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs