Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component

2014/09/29 by J. Inglis, Inglis, James, Denis Talay +1 · 2 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #stochastic dynamics and bifurcation #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.1409.8221

Abstract

In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior of a network of neurons, in which a classical noisy integrate-and-fire model is coupled with a cable equation to describe the dendritic structure of each neuron.

Cited by

• Mean Field Dynamics of a Network of Wilson-Cowan Neurons with Electrical\n Synapses
• Free boundary regularity and well-posedness of physical solutions to the supercooled Stefan problem

Related

• Analysis of a mean-field limit of interacting two-dimensional nonlinear integrate-and-fire neurons
• Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling
• Mean-field analysis of a neural network with stochastic STDP
• The mean-field Limit of sparse networks of integrate and fire neurons
• Long run convergence of discrete-time interacting particle systems of the McKean-Vlasov type