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Qualitative properties of chemostat equations with time delays: Boundedness, local and global asymptotic stability. (English) Zbl 0868.45002
Summary: A chemostat model with continuous time delays for a nutrient recycling process and for a biotic species growth is considered. After showing the fundamental properties such as existence, uniqueness, positivity and boundedness of the solutions, the local asymptotic stability of a positive equilibrium point is proved under the general assumption on delay kernels. Further, two different global stability conditions are obtained for the model with a Lotka-Volterra coupling between nutrient and a biotic species and with an instantaneous response in the growth process.

45J05 Integro-ordinary differential equations
92E20 Classical flows, reactions, etc. in chemistry
92C40 Biochemistry, molecular biology
45M05 Asymptotics of solutions to integral equations
45M10 Stability theory for integral equations