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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

Competition between two similar species in the unstirred chemostat

Pages: 621 - 639, Volume 21, Issue 2, March 2016      doi:10.3934/dcdsb.2016.21.621

 
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Hua Nie - College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710119, China (email)
Yuan Lou - Institute for Mathematical Sciences, Renmin University of China, Haidian District, Beijing, 100872, China (email)
Jianhua Wu - College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710119, China (email)

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.

Keywords:  Unstirred chemostat, coexistence solution, stability, Lyapunov-Schmidt reduction, perturbation.
Mathematics Subject Classification:  Primary: 35K57, 35B32; Secondary: 92D25.

Received: January 2015;      Revised: May 2015;      Available Online: November 2015.

 References