Noise-induced stochastic transition: A stochastic chemostat model with two complementary nutrients and flocculation effect

Abstract

A novel stochastic chemostat model with two complementary nutrients and flocculation effect is considered in this paper. Firstly, the well-posedness of the stochastic chemostat model is considered. Then, by constructing appropriate stochastic Lyapunov functions, some sufficient conditions for the existence of an ergodic stationary distribution and persistence of the stochastic model are given. The results show that the microorganisms in chemostat can be collected continuously. Furthermore, based on sensitivity analysis techniques, some control strategies are discussed. Finally, we carry out some numerical simulations to illustrate the applications of theoretical results and give the empirical probability densities in numerical forms. In particular, the numerical simulations show that, when the random fluctuation of the environment is large, the growth of the microorganisms in chemostat can be transformed from the state of tending to extinction to the state of persistence. The interesting observation reveals that the random fluctuation may have positive biological effects and we call it the noise-induced stochastic transition phenomenon.