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

Further studies of a reaction-diffusion system for an unstirred chemostat with internal storage

Pages: 3169 - 3189, Volume 19, Issue 10, December 2014      doi:10.3934/dcdsb.2014.19.3169

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Sze-Bi Hsu - Department of Mathematics and The National Center for Theoretical Science, National Tsing-Hua University, Hsinchu 30013, Taiwan (email)
Junping Shi - Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795, United States (email)
Feng-Bin Wang - Department of Natural Science in the Center for General Education, Chang Gung University, Kwei-Shan, Taoyuan 333, Taiwan (email)

Abstract: The dynamics of a reaction-diffusion system for two species of microorganism in an unstirred chemostat with internal storage is studied. It is shown that the diffusion coefficient is a key parameter of determining the asymptotic dynamics, and there exists a threshold diffusion coefficient above which both species become extinct. On the other hand, for diffusion coefficient below the threshold, either one species or both species persist, and in the asymptotic limit, a steady state showing competition exclusion or coexistence is reached.

Keywords:  Unstirred chemostat, reaction-diffusion system, internal storage, steady state.
Mathematics Subject Classification:  35K51, 35K57, 35B35, 92D25.

Received: June 2013;      Revised: August 2013;      Available Online: October 2014.