Global asymptotic stability of the periodic Lotka-Volterra system with two predators and one prey
type: Item
instance of: scholarly article
title: Global asymptotic stability of the periodic Lotka-Volterra system with two predators and one prey
zbMATH Open document ID: 0840.34036
DOI: 10.1007/BF02662869
author: Z. H. Lu
author: Lansun Chen
published in: Applied Mathematics. Series B (English Edition)
publication date: 1996-07-04T00:00:00Z
review text: The authors consider the three species Lotka-Volterra periodic model with two predators and one prey \[ \dot x_i= x_i[\delta_i(b_i(t)- a_{i1}(t))x_1- a_{i2}(t) x_2- a_{i3}(t) x_3],\tag{1} \] where \(\delta_1= 1= -\delta_2= -\delta_3\), \(a_{23}(t)= a_{32}(t)= 0\), \(i= 1, 2, 3\). Suppose that the functions \(b_i(t)\), \(a_{ij}(t)\), \(i,j= 1, 2, 3\) are continuous, nonnegative and periodic functions with a common period \(T> 0\) and \(b_1(t)\), \(a_{ii}(t)\), \(i= 1, 2, 3\) are strictly positive. By using Brouwer's fixed point theorem, the authors show that the system (1) has at least one strictly positive \(T\)-periodic solution, if the coefficients of (1) satisfy some conditions. The authors also give some sufficient conditions to guarantee that a unique strictly positive solution of (1) is globally asymptotically stable.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 840329
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: periodic solution
zbMATH Keywords: three species Lotka-Volterra periodic model with two predators and one prey
Wikidata QID: Q115609842
reviewed by: Jibin Li
MaRDI profile type: Publication
cites work: Q4698441
cites work: Q5533446
cites work: Global asymptotic stability in a periodic Lotka-Volterra system
cites work: Exchange of equilibria in two species Lotka-Volterra competition models
full work available at URL: https://doi.org/10.1007/bf02662869
OpenAlex ID: W2317041005
description: scientific article; zbMATH DE number 840329