Feedback control for nonmonotone competition models in the chemostat

被引：39

作者：

Gouzé, JL ^{[1
]}

Robledo, G ^{[1
]}

机构：

[1] INRIA, Project COMORE, F-06902 Sophia Antipolis, France

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2005年 / 6卷 / 04期

关键词：

chemostat; nonmonotone growth functions; competition model; feedback control; competitive dynamical systems; global stability;

D O I：

10.1016/j.nonrwa.2004.12.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the problem of feedback control of competition between two species with one substrate in the chemostat with nonmonotone growth functions. Without control, the generic behavior is competitive exclusion. The aim of this paper is to find a feedback control of the dilution rate, depending only on the total biomass, such that coexistence holds. We obtain a sufficient condition for the global asymptotic stability of a unique equilibrium point in the positive orthant for a three-dimensional differential system which arises from this controlled competition model. This paper generalizes the results obtained by De Leenheer and Smith in (J. Math. Biol. 46 (2003) 48). (c) 2004 Elsevier Ltd. All rights reserved.

引用

页码：671 / 690

页数：20

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