Permanence and global stability in a Lotka-Volterra predator-prey system with delays
type: Item
instance of: scholarly article
title: Permanence and global stability in a Lotka-Volterra predator-prey system with delays
zbMATH Open document ID: 1054.34127
DOI: 10.1016/S0893-9659(03)90124-8
author: Yoshiaki Muroya
published in: Applied Mathematics Letters
publication date: 2004-06-15T00:00:00Z
review text: The author considers permanence and global asymptotic stability of models governed by the following Lotka-Volterra-type system \[ \dot x_{i}(t)=x_{i}(t)\{r_{i}-\alpha_{i}x_{i}(t)-a_{i}x_{i-1}(t- \tau_{i,i-1})-b_{i}x_{i}(t-\tau_{i,i})-c_{i}x_{i+1}(t- \tau_{i,i+1})\}, \] \(t\geq t_{0},1\leq i\leq n,\) with the initial conditions \[ x_{i}(t)=\phi_{i}(t)\geq 0,\;t\leq t_{0},\;\text{ and } \phi_{i} (t_{0})>0,\;1\leq i\leq n, \] where \(x_{0}(t)=x_{n+1}(t)\equiv 0\) and \(\phi_{i}(t),\;1\leq i\leq n\), are bounded continuous functions on \([t_{0},+\infty)\) and \(r_{i}>0\), \(\alpha_{i}>0\), \(c_{i}>0\), \(\tau_{i,j}\geq 0\), for all relevant \(i,\;j\). The author derives sufficient conditions for permanence and global asymptotic stability of solutions.
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2075535
zbMATH Keywords: permanence
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: Lotka-Volterra predator-prey system
reviewed by: Lansun Chen
MaRDI profile type: Publication
Wikidata QID: Q115564143
cites work: Necessary and sufficient conditions for permanence and global stability of a Lotka-Volterra system with two delays
cites work: Global asymptotic stability in Volterra's population systems
cites work: The necessary and sufficient condition for global stability of a Lotka-Volterra cooperative or competition system with delays
cites work: Persistence and global stability for a delayed nonautonomous predator-prey system without dominating instantaneous negative feedback
full work available at URL: s0893-9659(03)90124-8
OpenAlex ID: W2058732322
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description: scientific article; zbMATH DE number 2075535