The effect of inhibitor on the plasmid-bearing and plasmid-free model in the unstirred chemostat

• Published in: SIAM journal on mathematical analysis Vol. 38; no. 6; pp. 1860 - 1885
• Main Authors: JIANHUA WU, HUA NIE, WOLKOWICZ, Gail S. K
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 2007
• Subjects: Applied mathematics; Competition; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematics; Operator theory; Organisms; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Perturbation theory; Solution uniqueness; Growth rate; 35K57,35J65; Bifurcation theory; Degree theory; Steady state; 35K55; chemostat; Sufficient condition; 92A17; Perturbation techniques; coexistence solution; Numerical stability; stability; Maximal solution
• DOI: 10.1137/050627514
• ISSN: 0036-1410

This paper deals with a chemostat model with an inhibitor in the context of competition between plasmid-bearing and plasmid-free organisms. First, sufficient conditions for coexistence of the steady-state are determined. Second, the effects of the inhibitor are considered. It turns out that the parameter μ, which represents the effect of the inhibitor, plays a very important role in deciding the number of the coexistence solutions. The results show that if μ is sufficiently large this model has at least two coexistence solutions provided that the maximal growth rate $a$ of $u$ lies in a certain range and has only one unique asymptotically stable coexistence solution when $a$ belongs to another range. Finally, extensive simulations are done to complement the analytic results. The main tools used here include degree theory in cones, bifurcation theory, and perturbation technique.