Analysis of a model of two competitors in a chemostat with an external inhibitor.

*(English)*Zbl 0788.34040Summary: A model of the chemostat with an external nutrient and an external inhibitor is considered. A preliminary analysis reduces the problem to a three-dimensional competitive system. The theory of monotone flows is applied to obtain several global results. Global results fail when questions of multiple limit cycles cannot be answered. An example of an attracting limit cycle is given.

The chemostat with inhibitor can model competition between two populations of microorganisms, where one strain is resistant to an antibiotic or competition in detoxification, a system where one strain can take up the pollutant while the other is inhibited by it.

The chemostat with inhibitor can model competition between two populations of microorganisms, where one strain is resistant to an antibiotic or competition in detoxification, a system where one strain can take up the pollutant while the other is inhibited by it.

Reviewer: Reviewer (Berlin)

##### MSC:

37-XX | Dynamical systems and ergodic theory |

92D40 | Ecology |

34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |