The effect of inhibitor on the plasmid-bearing and plasmid-free model in the unstirred chemostat
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 para...
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Published in | SIAM journal on mathematical analysis Vol. 38; no. 6; pp. 1860 - 1885 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Philadelphia, PA
Society for Industrial and Applied Mathematics
2007
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0036-1410 1095-7154 |
DOI: | 10.1137/050627514 |