Long-Time Behavior of a Stochastic Turbidostat Model Under Degenerate Diffusion

Due to many uncertain factors,parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental fluctuation.In this paper,the authors develop a stochastic turbidostat model that considers white noise,formulate and analyze dynamical behavior for the stochastic model.The authors obtain the existence and uniqueness of globally positive equilibrium.Sufficient conditions of the extinction for the system are established.Since the uniformly elliptic condition can fail to satisfy,the existence of the stationary distribution of the system is proved by using Markov semigroups theory.Biologically speaking,the existence of stationary distribution suggests that microorganism will exist for a long time.The analytical results are tested and verified by numerical simulations,which evaluate the influence of white noise on the dynamics of microorganism.