Delayed feedback control for a chemostat model

In this paper, we discuss asymptotic properties and numerical simulations of a chemostat model with delayed feedback control. A chemostat model with two organisms can be made coexistent by feedback control of the dilution rate which depends affinely on the concentrations of two organisms [P. De Leenher, H.L. Smith, Feedback control for chemostat models, J. Math. Biol. 46 (2003) 48]. Then the coexistence takes its simplest form; the equilibrium point in the non-negative orthant is globally asymptotically stable. We show that stability of the equilibrium point is changed by 'time-delay' caused in controlling the dilution rate after measuring the concentrations of two organisms.