Author(s)

Tawfiqullah Ayoubi

School of Mathematics and Statistics, Southwest University, Chongqing, China.

Current research is concerned with the stability of stochastic logistic equation with Ornstein-Uhlenbeck process. First, this research proves that the stochastic logistic model with Ornstein-Uhlenbeck process has a positive solution. After that, it also introduces the sufficient conditions for stochastically stability of stochastic logistic model for cell growth of microorganism in fermentation process for positive equilibrium point by using Lyapunov function. In addition, this research establishes the sufficient conditions for zero solution as mentioned in Appendix A due to the cell growth of microorganism μ_max, which cannot be negative in fermentation process. Furthermore, for numerical simulation, current research uses the 4-stage stochastic Runge-Kutta (SRK4) method to show the reality of the results.

Stability, Fermentation Process, Ornstein-Uhlenbeck Process, Logistic Model, Lyapunov Function, 4-Stage Stochastic Runge-Kutta Method

Ayoubi, T. (2019) Stability of Stochastic Logistic Model with Ornstein-Uhlenbeck Process for Cell Growth of Microorganism in Fermentation Process. Applied Mathematics, 10, 659-675. doi: 10.4236/am.2019.108047.