Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons

摘要: ABSTRACT: We derive the mean-field equations arising as limit of a network interacting spiking neurons, number neurons goes to infinity. The belong fixed populations and are represented either by Hodgkin-Huxley model or one its simplified version, FitzHugh-Nagumo model. synapses between electrical chemical. is assumed be fully connected. maximum conductances vary randomly. Under condition that all neurons' initial conditions drawn independently from same law depends only on population they to, we prove propagation chaos phenomenon takes place, namely in limit, any finite become independent and, within each population, have probability distribution. This distribution solution set implicit equations, nonlinear stochastic differential resembling McKean-Vlasov non-local partial McKean-Vlasov-Fokker-Planck equations. wellposedness i.e. existence uniqueness solution. also show results some numerical experiments indicate good representation mean activity size network, even for modest sizes. These may way understand dynamics through, e.g. bifurcation analysis.