Competition between two similar species in the unstirred chemostat

Hua  Nie; Yuan Lou; Jianhua  Wu

doi:10.3934/dcdsb.2016.21.621

Article Contents

2016, Volume 21, Issue 2: 621-639. Doi: 10.3934/dcdsb.2016.21.621

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Competition between two similar species in the unstirred chemostat

1.
College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710119
2.
Institute for Mathematical Sciences, Renmin University of China, Haidian District, Beijing, 100872

Received: December 31, 2014

Revised: April 30, 2015

Published: February 2016

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Abstract

This paper deals with the competition between two similar species in the unstirred chemostat. Due to the strict competition of the unstirred chemostat model, the global dynamics of the system is attained by analyzing the equilibria and their stability. It turns out that the dynamics of the system essentially depends upon certain function of the growth rate. Moreover, one of the semi-trivial stationary solutions or the unique coexistence steady state is a global attractor under certain conditions. Biologically, the results indicate that it is possible for the mutant to force the extinction of resident species or to coexist with it.

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Mathematics Subject Classification: Primary: 35K57, 35B32; Secondary: 92D25.

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