Qualitative properties of chemostat equations with time delays. II
type: Item
instance of: scholarly article
title: Qualitative properties of chemostat equations with time delays. II
zbMATH Open document ID: 0995.34068
author: E. Beretta
author: Yasuhiro Takeuchi
published in: Differential Equations and Dynamical Systems
publication date: 2002-10-15T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34K60
zbMATH DE Number: 1014345
zbMATH Keywords: time delay
zbMATH Keywords: chemostat
zbMATH Keywords: global stability
reviewed by: Marcos Lizana
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1014345