Chemostat — Monod Growth Kinetics

dX/dt = (μ−D)X, dS/dt = D(S₀−S) − μX/Y, μ = μ_max·S/(K_s+S)

Steady state — S*: —  |  X*: —  |  —
In a chemostat, bacteria grow on a limiting nutrient S with Monod kinetics. Steady state: S* = K_s·D/(μ_max−D), X* = Y(S₀−S*)/1. If D > μ_max (washout): bacteria cannot grow fast enough and are diluted out — X→0. The washout transition is a sharp threshold. S₀=1 (feed concentration), Y=0.5 (yield).