Global attractivity in a competition system with feedback controls.
type: Item
instance of: scholarly article
title: Global attractivity in a competition system with feedback controls.
zbMATH Open document ID: 1059.93111
DOI: 10.1016/S0898-1221(03)00026-9
publication date: 2003-12-14T00:00:00Z
review text: The authors consider a two species Lotka-Volterra competition system with feedback controls. They derive sufficient conditions for the existence of a globally attracting positive equilibrium in the cases where the indirect controls act instantaneously or with a fixed time delay \(\tau\). These cases are modeled respectively by the systems \[ \begin{aligned} {dx_1(t)\over dt} &=x_1(t)\{b_1-a_{11}x_1(t)-a_{12}x_2(t)-\alpha_1 u_1(t)\},\\ {dx_2(t)\over dt} &=x_2(t)\{b_2-a_{21}x_1(t)-a_{22}x_2(t)-\alpha_2 u_2(t)\},\\ {du_1(t)\over dt} &=-\eta_1u_1(t)+a_1x_1(t),\\ {du_2(t)\over dt} &=-\eta_2u_2(t)+a_2x_2(t),\\ \text{and} {dx_1(t)\over dt} &=x_1(t)\{b_1-a_{11}x_1(t)-a_{12}x_2(t)-\alpha_1 u_1(t-\tau)\},\\ {dx_2(t)\over dt} &=x_2(t)\{b_2-a_{21}x_1(t)-a_{22}x_2(t)-\alpha_2 u_2(t-\tau)\},\\ {du_1(t)\over dt} &=-\eta_1u_1(t)+a_1x_1(t-\tau),\\\;{du_2(t)\over dt} &=-\eta_2u_2(t)+a_2x_2(t-\tau). \end{aligned} \]
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 2017218
zbMATH Keywords: Lotka-Volterra competition system
zbMATH Keywords: feedback control
zbMATH Keywords: global attractivity
zbMATH Keywords: stabilization
zbMATH Keywords: delay
author: K. Gopalsamy
author: Peixuan Weng
reviewed by: Vigirdas Mackevičius
MaRDI profile type: Publication
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full work available at URL: s0898-1221(03)00026-9
OpenAlex ID: W2044697359
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2017218