On the positive almost periodic solutions of a class of Lotka-Volterra type systems with delays
type: Item
instance of: scholarly article
title: On the positive almost periodic solutions of a class of Lotka-Volterra type systems with delays
zbMATH Open document ID: 0967.34064
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-08-30T00:00:00Z
review text: The following almost-periodic Lotka-Volterra type systems with delays are investigated \[ {dx_i(t)\over dt}= x_i(t)(a_i(t)- b_i(t) x_i(t)- f_i(t, x_t)),\quad i= 1,2,\dots, n,\tag{1} \] with \(t\in\mathbb{R}\), \(x(t)= (x_1(t),x_2(t),\dots, x_n(t))\in \mathbb{R}^n\), \(x_t= (x_{1t}, x_{2t},\dots, x_{nt})\in C^n[-\tau, 0]\), and \(x_{it}(s)= x_i(t+ s)\), \(i= 1,2,\dots, n\), for all \(s\in [-\tau,0]\); \(a_i(t)\) and \(b_i(t)\) are continuous almost-periodic functions with respect to \(t\in \mathbb{R}\) and \(b_i(t)\geq 0\) for all \(t\in\mathbb{R}\). The author establishes a general criterion for the existence of positive almost-periodic solutions to system (1). The conditions required in the criterion are quite weak, and can be easily checked and reduced to some well-known results.
Mathematics Subject Classification ID: 34K14
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 1533176
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: almost-periodic system with delay
zbMATH Keywords: almost-periodic solution
author: Zhidong Teng
reviewed by: Lansun Chen
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6891
OpenAlex ID: W2048272923
cites work: On the nonautonomous N-competing species problems
cites work: Asymptotically periodic solutions of \(N\)-competing species problem with time delays
cites work: Global asymptotic stability in a nonautonomous Lotka-Volterra type system with infinite delay
cites work: Almost periodic differential equations
cites work: The existence of almost periodic solution of a population equation with delay
cites work: Almost periodic solutions for delay logistic equations with almost periodic time dependence
cites work: On the asymptotic behavior of some population models
DOI: 10.1006/JMAA.2000.6891
Recommended article: The positive periodic solutions to a class of periodic Lotka-Volterra-type systems with infinite delay
Recommended article: Q3572510
Recommended article: Q5371528
Recommended article: Q5490871
Recommended article: Positive periodic solutions of delayed periodic Lotka-Volterra systems
Recommended article: On the positive almost periodic solutions of a class of nonlinear Lotka-Volterra type systems
Recommended article: Q3596414
Recommended article: Almost periodic solutions for Lotka-Volterra systems with delays
Recommended article: Existence of positive periodic solution of \(n\)-dimensional Lotka-Volterra system with delays
Recommended article: Existence of Positive Periodic Solutions of a Lotka-Volterra System with Multiple Time Delays
description: scientific article; zbMATH DE number 1533176