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A SYSTEM OF REACTION–DIFFUSION EQUATIONS IN THE UNSTIRRED CHEMOSTAT WITH AN INHIBITOR

HUA NIE

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China

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JIANHUA WU

College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China

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https://doi.org/10.1142/S0218127406015246Cited by:24 (Source: Crossref)

Abstract

A system of reaction–diffusion equations is considered in the unstirred chemostat with an inhibitor. Global structure of the coexistence solutions and their local stability are established. The asymptotic behavior of the system is given as a function of the parameters, and it is determined when neither, one, or both competing populations survive. Finally, the results of some numerical simulations indicate that the global stability of the steady-state solutions is possible. The main tools for our investigations are the maximum principle, monotone method and global bifurcation theory.

The work is supported by the Natural Science Foundation of China (Nos. 10571115, 10071048), the Excellent Young Teachers Program by the Ministry of Education of China and the Innovation Foundation of Shaanxi Normal University.

Keywords:

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