Global asymptotic behavior of an aquatic system with periodic nutrient supply

Abstract

We study the dynamical properties of a chemostat model in which two species compete for a periodically supplied, growth-limiting nutrient. We exploit the well known basic properties of the model to study the behaviour in an aquatic system. This dissertation contains six chapters: the introduction, literature review and four other chapters. The introduction in chapter one deals with the assumptions and basic properties that justify formulation of a chemostat model. In chapter two, we review what has been done. We review the analysis of models incorporatinq. either constant or periodic parameters, inhibition factors as well as tkne delays. In chapter three, we provide the necessary results and boundedness t.o have. the model meaningful. This chapter is based on the assumption thatthe nutrient is supplied at a constant rate. In chapter four we extend the results in chapter three to study a system in which the nutrient supply varies with time. In chapter five, we numerically demonstrate thebebaviour of solutions of chapter four. Chapter six is the conclusion.