Periodic solutions of nonautonomous stage-structured cooperative system
type: Item
instance of: scholarly article
title: Periodic solutions of nonautonomous stage-structured cooperative system
zbMATH Open document ID: 1069.34066
DOI: 10.1016/S0898-1221(04)90057-0
author: Zhengqiu Zhang
author: Jun Wu
author: Zhicheng Wang
publication date: 2005-03-08T00:00:00Z
review text: The purpose of this note is to study the stage-structured nonautonomous cooperative system of species \[ \begin{gathered} \dot x_1(t)= \alpha(t)x_2(t)- r_1(t)x_1(t)- x_1(t)- \eta_1(t)x^2_1(t),\\ \dot x_2(t)= \beta(t)x_1(t)- r_2(t)x_2(t) - \eta_2(t)x^2_2(t)+ b(t)x_2(t)y(t),\\ \dot y(t)= y(t) [R(t)- a(t)y(t)+ c(t)x_2(t)],\end{gathered}\tag{\(*\)} \] where \(\alpha(t)\), \(\beta(t)\), \(r_i(t)\), \(\eta_i(t)\), \(i= 1,2\), \(a(t)\), \(b(t)\), \(c(t)\) and \(R(t)\) are positive periodic continuous functions with period \(\omega> 0\). The authors prove the existence of a positive \(\omega\)-periodic solution of system \((*)\). The method used is based on the continuation theorem of coincidence degree theory.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2142338
zbMATH Keywords: Stage-structured and cooperative system
zbMATH Keywords: periodic solution
zbMATH Keywords: continuation theorem
zbMATH Keywords: topological degree theory
MaRDI profile type: Publication
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142338