Persistence in a large network of sparsely interacting neurons

Maximiliano Altamirano, Roberto Cortez, Matthieu Jonckheere, Lasse Leskelä

Producción científica: Contribución a una revistaArtículorevisión exhaustiva


This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of sparse interactions: each firing neuron triggers an instantaneous increase in electric potential to a fixed number of randomly chosen neurons. We prove that, as the number of neurons approaches infinity, the finite network converges to a nonlinear mean-field process characterised by a jump-type stochastic differential equation. We show that this process displays a phase transition: the activity of a typical neuron in the infinite network either rapidly dies out, or persists forever, depending on the global parameters describing the intensity of interconnection. This provides a way to understand the emergence of persistent activity triggered by weak input signals in large neural networks.

Idioma originalInglés
Número de artículo16
PublicaciónJournal of Mathematical Biology
EstadoPublicada - ene. 2023

Áreas temáticas de ASJC Scopus

  • Modelización y simulación
  • Agricultura y biología (miscelánea)
  • Matemáticas aplicadas


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