Global periodic solutions for a differential delay system modeling a microbial population in the chemostat
The author studies the differential delay system modeling a microbial population in the chemostat \[ \dot s(t)= 1- s(t)- P(s(t))u(t),\quad \dot u(t)= [- 1+ P(S((t- \tau))].\tag{1} \] The author gives a sufficient conditions that the washout steady state (\(u= 0\), \(S= 1\)) is globally stable and establishes sufficient conditions for the global existence of a periodic solution by proving the existence of nontrivial periodic points of an appropriate map. The author also presents an explicit application to Michaelis-Menten kinetics.
scientific article; zbMATH DE number 811591