Phase Transition for Infinite Systems of Spiking Neurons

Autor(es)

Ferrari, P. A. ^[1] ; Galves, A. ^[2] ; Grigorescu, I ^[3] ; Locherbach, E. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Buenos Aires, Buenos Aires, DF - Argentina

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

^[3] Univ Miami, Coral Gables, FL 33124 - USA

^[4] Univ Paris Seine, Cergy - France

• Tipo de documento: Artigo Científico
• Fonte: Journal of Statistical Physics; v. 172, n. 6, p. 1564-1575, SEP 2018.
• Citações Web of Science: 1

Resumo

We prove the existence of a phase transition for a stochastic model of interacting neurons. The spiking activity of each neuron is represented by a point process having rate 1 whenever its membrane potential is larger than a threshold value. This membrane potential evolves in time and integrates the spikes of all presynaptic neurons since the last spiking time of the neuron. When a neuron spikes, its membrane potential is reset to 0 and simultaneously, a constant value is added to the membrane potentials of its postsynaptic neurons. Moreover, each neuron is exposed to a leakage effect leading to an abrupt loss of potential occurring at random times driven by an independent Poisson point process of rate gamma > 0. For this process we prove the existence of a value gamma(c) such that the system has one or two extremal invariant measures according to whether gamma > gamma(c) or not. (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