Uniqueness of positive steady state solutions to the unstirred chemostat model with external inhibitor

Hua Nie; Wenhao Xie; Jianhua Wu

doi:10.3934/cpaa.2013.12.1279

Article Contents

2013, Volume 12, Issue 3: 1279-1297. Doi: 10.3934/cpaa.2013.12.1279

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Uniqueness of positive steady state solutions to the unstirred chemostat model with external inhibitor

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710062
2.
School of Science, Xi'an Shiyou University, Xi'an, Shaanxi 710065
3.
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, Shaanxi 710119

Received: December 31, 2011

Revised: July 31, 2012

Published: April 2013

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Abstract

A competition model of two organisms is considered in the un-stirred chemostat-type system in the presence of an external inhibitor. Asymptotic stability properties of the trivial and semi-trivial steady state solutions are established by spectral analysis. The stability and uniqueness of positive steady state solutions are also given by Lyapunov Schmidt procedure and perturbation technique.

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Mathematics Subject Classification: Primary: 35K55, 35K57; Secondary: 92A17.

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