Positive periodic solution for a nonautonomous logistic model with linear feedback regulation
type: Item
instance of: scholarly article
title: Positive periodic solution for a nonautonomous logistic model with linear feedback regulation
zbMATH Open document ID: 1116.34052
author: Xiaoquan Ding
author: Shuhan Cheng
published in: Applied Mathematics. Series B (English Edition)
publication date: 2006-12-05T00:00:00Z
review text: The authors considered the following nonautonomous logistic model with linear feedback regulation \[ \begin{aligned} & x_1'(t)=x_1(t)\bigl(r(t)-a_1 (t)x_1(t)-a_2(t) x_1(t-\tau_1)-c(t)x_2(t-\tau_2)\bigr),\\ & x_2'(t)=-a(t) x_2(t)+b(t)x_1(t-\tau_3), \end{aligned}\tag{*} \] with initial condition: \[ x_i(\theta)=\psi_i (\theta),\theta\in[-\tau,0],\;\psi_i(0)\geq 0,\psi_i\in C^1\bigl([-\tau,0],R_+ \bigr),\;i=1,2, \] where \(a(t)\), \(b(t)\), \(c(t)\), \(r(t)\), \(a_1(t)\) and \(a_2(t)\) are continuous \(\omega\)-periodic functions; \(a(t)\), \(b(t)\), \(c(t)\) and \(r(t)\) are strictly positive, \(a_1(t)\) and \(a_2 (t)\) are nonnegative, \(\tau_1\), \(\tau_2\) and \(\tau_3\) are nonnegative constants, \(\tau=\max\{\tau_1,\tau_2,\tau_3\}\). The authors establish sufficient conditions for the uniform persistence of the model and for existence, uniqueness and global asymptotic stability of a positive \(\omega\)-periodic solution of the system (*), respectively.
reviewed by: He Chungyou
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 5077205
zbMATH Keywords: nonautonomous delayed logistic model
zbMATH Keywords: positive solution
zbMATH Keywords: uniform persistence
zbMATH Keywords: global stability
MaRDI profile type: Publication
full work available at URL: s11766-003-0006-5
OpenAlex ID: W1976430685
cites work: Q4003237
cites work: Feedback regulation of logistic growth
cites work: Q4880276
cites work: Q3147956
cites work: Harmless delays for uniform persistence
cites work: Coincidence degree, and nonlinear differential equations
DOI: 10.1007/S11766-003-0006-5
description: scientific article; zbMATH DE number 5077205