Global stability in a periodic delayed predator-prey system
type: Item
instance of: scholarly article
title: Global stability in a periodic delayed predator-prey system
zbMATH Open document ID: 1122.34048
author: Zhijun Liu
author: Ronghua Tan
author: Lansun Chen
published in: Applied Mathematics and Computation
publication date: 2007-04-26T00:00:00Z
review text: The authors study existence and global attractivity of a positive periodic solution of the periodic delayed predator-prey system \[ \begin{aligned} y_1'(t)&=y_1(t)\left[r_1(t)-a_1(t)y_1(t)+\sum_{i=1}^nb_{1i}(t)y_1(t-\tau_i(t))-\sum_{j=1}^mc_{1j}(t) y_2(t-\rho_{j}(t))\right],\\ y_2'(t)&=y_2(t)\left[r_2(t)-a_2(t)y_2(t)+\sum_{j=1}^mb_{2j}(t)y_2(t-\eta_j(t))+\sum_{i=1}^nc_{2i}(t) y_1(t-\sigma_{i}(t))\right]. \end{aligned}\tag{1} \] By using the method of coincidence degree and a Lyapunov functional, under some assumptions, easily verifiable sufficient conditions are obtained for the existence and global attractivity of a positive periodic solution of (1). Biological interpretations on the main results are also given.
reviewed by: Jurang Yan
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 5147014
zbMATH Keywords: positive periodic solution
zbMATH Keywords: global asymptotic stability
zbMATH Keywords: delay predator-prey system
zbMATH Keywords: coincidence
zbMATH Keywords: Lyapunov functional
MaRDI profile type: Publication
full work available at URL: j.amc.2006.07.123
OpenAlex ID: W1964273697
Wikidata QID: Q115598612
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DOI: 10.1016/J.AMC.2006.07.123
description: scientific article; zbMATH DE number 5147014