2021/08/13 by Maximiliano Altamirano, Roberto Cortez, Altamirano, Maximiliano +5
Computer Science · Neuroscience · Physics and Astronomy · #FOS: Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #Probability (math.PR) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2108.06386
openalex publication_date 2021/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 local 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 meanfield 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.