Characterization with Fokker–Planck theory of the nonlinear stochastic dynamics of a class of two-state continuous bioreactors

The nonlinear stochastic dynamics of a class of two-state bioreactors with isotonic or nonisotonic kinetics is analytically characterized with Fokker–Planck (FP) theory, with emphasis on: (i) the spatiotemporal geometry of the two-state probability density function (PDF) motion, (ii) conditions for metastability-based bio-extinction/revival (inexistent in deterministic systems), and (iii) state PDF behavior of the optimal (maximum yield) operation. It is found that, depending on the kind of kinetics: (i) the stationary state PDF is mono or bimodal, (ii) the state PDF motions can be either non-metastable along deterministic-diffusion time scale, or metastable towards probabilistic extinction/revival along deterministic-diffusion-escape time scale, and (iii) the optimal operation can have robust (or fragile) stationary PDF, depending on the particular kinetics and operation condition. The developments and results are illustrated with representative examples with Monod and Haldane kinetics, and put in perspective with the ones drawn before with Monte Carlo (MC) and FP methods.