Competition in the chemostat: A distributed delay model and its global asymptotic behavior.

*(English)*Zbl 0893.34067The authors study a two species competition model in a chemostat which uses a distributed delay to model the lag in the process of nutrient conversion. They give sufficient conditions under which both species go extinct, or one survives and one goes extinct. They prove a competitive exclusion principle which covers the situation in which either species could survive independently, but which states that only one can survive competition and determines which one that is. The main tool used is the so-called “linear chain trick” which allows one to convert the functional-differential equations into a higher order set of ordinary differential equations. However, this process requires that the kernels in the delay terms have a particular form.

Finally, the results of some numerical experiments are reported and a comparison is made between the distributed delay model, the discrete delay model, and the ordinary differential equation model.

Finally, the results of some numerical experiments are reported and a comparison is made between the distributed delay model, the discrete delay model, and the ordinary differential equation model.

Reviewer: A.Hausrath (Boise)

##### MSC:

34K20 | Stability theory of functional-differential equations |

92D25 | Population dynamics (general) |

34D20 | Stability of solutions to ordinary differential equations |

45M10 | Stability theory for integral equations |