Periodic Oscillations in a Chemostat Model with Two Discrete Delays

Abstract

Periodic oscillations of solutions of a chemostat-type model in which a species feeds on a limiting nutrient are considered. The model incorporates two discrete delays representing the lag in nutrient recycling and nutrient conversion. Through the study of characteristic equation associated with the linearized system, a unique positive equilibrium is found and proved to be locally asymptotically stable under some conditions. Meanwhile, a Hopf bifurcation causing periodic solutions is also obtained. Numerical simulations illustrate the theoretical results.