Analysis of a FitzHugh–Nagumo–Rall model of a neuronal network

Publisher Website
Google Scholar
Abstract
Pursuing an investigation started in (Math. Meth. Appl. Sci. 2007; 30:681–706), we consider a generalization of the FitzHugh–Nagumo model for the propagation of impulses in a network of nerve fibres. To this aim, we consider a whole neuronal network that includes models for axons, somata, dendrites, and synapses (of both inhibitory and excitatory type). We investigate separately the linear part by means of sesquilinear forms, in order to obtain well posedness and some qualitative properties. Once they are obtained, we perturb the linear problem by a nonlinear term and we prove existence of local solutions. Qualitative properties with biological meaning are also investigated. Copyright © 2007 John Wiley & Sons, Ltd.

This publication has 28 references indexed in Scilit: