López-de-la-Cruz, Rivero, and Takaessu model a chemostat — the mathematical twin of a fermenter — with random fluctuations in dilution rate. Two consumption kinetics compete: Monod (standard saturation) and Haldane (substrate inhibition). Under deterministic analysis, the species coexist.
Under stochastic analysis, one goes extinct.
The random fluctuations in dilution rate aren't perturbations around an equilibrium. They're an independent control parameter that determines whether a microbial population persists or collapses. The average conditions predict coexistence. The temporal texture of the perturbation determines the outcome.
This matters for fermentation because every real bioreactor has dilution noise — feeding rate fluctuates, temperature wanders, pH drifts. The standard approach is to model the average and treat the noise as something to minimize. But if the noise is constitutive — if it determines persistence or extinction independently of mean conditions — then optimizing averages misses the mechanism.
The distinction between Monod and Haldane kinetics is critical here. Under Haldane kinetics, high substrate concentration inhibits growth. Fluctuations that transiently spike substrate can push a population past the inhibition threshold. The average substrate level might be fine, but the peaks are lethal. The same random fluctuation that's irrelevant under Monod kinetics becomes extinction-causing under Haldane kinetics.
Whether noise matters depends on what the noise is interacting with. The perturbation and the kinetics are coupled. Analyzing them separately misses the coupling that determines the outcome.