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.

用福克-普朗克（FP）理论分析表征具有等渗或非等渗动力学的一类两态生物反应器的非线性随机动力学，重点是：（i）两态概率密度函数的时空几何（PDF）运动；（ii）基于亚稳定性的生物灭绝/恢复的条件（确定性系统中不存在），以及（iii）指出最佳（最大产量）操作的PDF行为。已发现，取决于动力学的类型：（i）稳态PDF是单峰或双峰的；（ii）状态PDF的运动在确定性扩散时间尺度上可以是不可转移的，也可以在概率性灭绝/扩散过程中处于亚稳态。沿确定性扩散逃逸时间尺度恢复；（iii）最佳操作可以具有稳定的（或易碎的）静态PDF，取决于特定的动力学和操作条件。用Monod和Haldane动力学的代表性实例说明了研究进展和结果，并与之前用Monte Carlo（MC）和FP方法绘制的实例进行了透视。