Global Periodic-Solutions for a Differential Delay System Modeling a Microbial Population in the Chemostat

We show that nonconstant periodic solutions of the delay-differential system modeling a microbial population in the chemostat Ṡ(t) = 1 − S(t) − p(S(t))u(t)u̇(t) = u(t)[−1 + p(S(t − τ))] exist whenever the positive equilibrium is unstable.