zbMATH — the first resource for mathematics

Qualitative properties of chemostat equations with time delays. II. (English) Zbl 0995.34068
A chemostat model with continuous time delays for a nutrient recycling process and for a biotic species growth is considered. The fundamental assumption on the model is that the biotic species contain a self-regulating term which accounts for a finite carrying capacity of the enviroment.
The authors show that the term can play an important role for the global stability of the model and extend the results obtained by the authors [Differ. Equ. Dyn. Syst. 2, No. 1, 19-40 (1994; Zbl 0868.45002)]. The authors prove the global stability for a partial feasible equilibrium. Further, two different global stability conditions for a positive equilibrium are obtained for the model by two different Krasovski-Lyapunov functionals.
Reviewer: M.Lizana (Merida)

34K20 Stability theory of functional-differential equations
92D25 Population dynamics (general)
34K60 Qualitative investigation and simulation of models involving functional-differential equations