Dynamic Study Of Stochastic Chemostat Model

The chemostat is used to study the growth of microbial populations under nutrient-restricted conditions,we analyze the interaction between microorganisms in the chemostat,and make qualitative and quantitative analysis of the growth process of microorganisms.The growth process of microorganisms will be affected by random factors such as temperature,humidity,and illumination,that is,they will be disturbed by white noise.Also,microbes are often disturbed by color noise,which can cause them to switch from one environmental state to another completely different environmental state.Therefore,it is more reasonable to consider white noise and color noise about the dynamic behavior of the chemostat.In this paper,we establish three types of stochastic chemostat models under Gaussian white noise and color noise.The main contents are as follows:1.Study the stochastic two-species competition chemostat model under regime switch-ing.We prove the solution is positive and global by constructing suitable Lyapunov function,and sufficient conditions to show two-species microorganisms become extinction and persis-tent in the mean.Theoretical results are verified numerically.2.Study the stochastic food chain chemostat model under regime switching.We prove the existence and uniqueness of the global positive solution.And investigate the extinction and persistence of the prey and predator populations.Moreover,necessary and sufficien-t criteria for the existence of a unique ergodic stationary distribution of the system are established.3.Global asymptotic behavior of a stochastic food chain chemostat model with time delay.First,we verify that there is unique global positive solution for any given initial conditions.Then,we study the dynamical behavior around the equilibrium E₀,(?) and E^*of its corresponding deterministic model.