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Global analysis of a model of plasmid-bearing, plasmid-free competition in a chemostat with inhibitions. (English) Zbl 0840.92028

Summary: A model of competition between plasmid-bearing and plasmid-free organisms in a chemostat was proposed in a paper of G. Stephanopoulis and G. Lapidus [Chem. Eng. Sci. 43, 49-57 (1988)]. The model was in the form of a system of nonlinear ordinary differential equations. Such models were relevant to commercial production by genetically altered organisms in continuous culture. The analysis there was local. The rigorous global analysis was done in a paper of S.-B. Hsu, P. Waltman and G. S. K. Wolkowicz [J. Math. Biol. 32, No. 7, 731-742 (1994; Zbl 0802.92027)]in the case of the uninhibited specific growth rates.
This paper provides a mathematically rigorous analysis of the global asymptotic behavior of the governing equations in the cases of combinations of inhibited and uninhibited specific growth rates.

MSC:

92D40 Ecology
37N99 Applications of dynamical systems
92C40 Biochemistry, molecular biology
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
37C75 Stability theory for smooth dynamical systems
34D05 Asymptotic properties of solutions to ordinary differential equations

Citations:

Zbl 0802.92027
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References:

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