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Global periodic solutions for a differential delay system modeling a microbial population in the chemostat. (English) Zbl 0833.34069

The author studies the differential delay system modeling a microbial population in the chemostat

s ˙(t)=1-s(t)-P(s(t))u(t),u ˙(t)=[-1+P(S((t-τ))]·(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.

MSC:
34K13Periodic solutions of functional differential equations
92D25Population dynamics (general)
34C25Periodic solutions of ODE