Stability in chemostat equations with delayed recycling (Q1116037)

Stability and boundedness of the solutions of the system: \[ \dot S=D(S^ 0-S)-mU(S)N+bD_ 1\int^{t}_{-\infty}F(t-\tau)N(\tau)d\tau, \] \[ \dot N=N[-(D+D_ 1)+m_ 1U(S)] \] are studied with a general normalized non-negative function F. The system describes the growth of microorganisms feeding on a limiting nutrient. Conditions for local stability of the positive equilibrium are provided, and the effect of time lags is discussed.