Dynamics of an almost periodic logistic integrodifferential equation
type: Item
instance of: scholarly article
title: Dynamics of an almost periodic logistic integrodifferential equation
zbMATH Open document ID: 0835.45004
author: Xue-Zhong He
author: K. Gopalsamy
published in: Methods and Applications of Analysis
publication date: 1996-03-26T00:00:00Z
review text: The paper deals with the logistic integrodifferential equation \(dN(t)/dt = N(t) [a(t) - b(t) \int^\infty_0\) \(K_\alpha(s)\) \(N(t - s) ds]\) on \((0, \infty)\), where \(a(t)\) and \(b(t)\) are scalar almost periodic functions, while \(K_\alpha (t)\) is piecewise continuous and integrable on \((0, \infty)\), \(\alpha\) is a nonnegative number. The first problem considered in the paper is the derivation of certain a priori bounds for the solutions. Then the existence of an almost periodic globally attracting solution is proven. The functions \(a(t)\) and \(b(t)\) are assumed to be positive (besides their almost periodicity), and further conditions are imposed on \(K_\alpha\). The analysis is carefully conducted. Solutions with or without level- crossing are then investigated and conditions are provided for the validity of such properties. Two examples and numerical simulation illustrate the theory.
Mathematics Subject Classification ID: 45J05
zbMATH DE Number: 798943
zbMATH Keywords: bounds for solutions
zbMATH Keywords: logistic integrodifferential equation
zbMATH Keywords: almost periodic globally attracting solution
zbMATH Keywords: numerical simulation
reviewed by: Constantin Corduneanu
MaRDI profile type: Publication
DOI: 10.4310/MAA.1995.V2.N1.A3
description: scientific article; zbMATH DE number 798943