Existence of wave front solutions of an integral differential equation in nonlinear nonlocal neuronal network
type: Item
instance of: scholarly article
title: Existence of wave front solutions of an integral differential equation in nonlinear nonlocal neuronal network
zbMATH Open document ID: 1474.45071
DOI: 10.1155/2014/753614
author: Linghai Zhang
author: Jie Yuan
author: Chaudry Masood Khalique
author: Lijun Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions). The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.
Mathematics Subject Classification ID: 45K05
Mathematics Subject Classification ID: 35R05
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 92C20
zbMATH DE Number: 7023021
Wikidata QID: Q59041250
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/753614
OpenAlex ID: W2165722330
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description: scientific article; zbMATH DE number 7023021