Dynamic Study Of Stochastic Plankton Model

Phytoplankton dynamics is a qualitative and quantitative analysis of the growth of plankton and the law of virus infection by studying the dynamic behavior of biological models and analyzing the interaction between nutrient-phytoplankton-zooplankton.However,due to the complexity of the ecosystem,both the growth process of plankton and the transmission process of viruses will be more or less disturbed by various environmental noises.In addition,plankton and virus infections are often highly disturbed.Disturbance will 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 when studying the dynamic behavior of plankton.In this paper,Gaussian white noise is described by Brownian motion,and Markov chain is used to describe color noise to establish three types of random plankton models.The main contents are as follows:1.Study on stochastic plankton model of toxin production is investigated.We prove the existence and uniqueness of the global positive solution,establish the threshold condition between the population's weakly persistence in mean and extinction,and prove the existence of unique ergodic stationary distribution of the system by constructing the lyapunov function.2.Positive recurrence of a stochastic plankton model with toxin-producing phytoplank-ton under regime switching.The existence of a unique global positive solution is proved by constructing an appropriate Liapunov function.By using Khasminskii's ergodic theorem,sufficient condition is established to prove that system is positive recurrence and ergodic.3.Researcher on stochastic phytoplankton model with viral infection and Markov switching.We get the critical value of whether or not the phytoplankton infected with the virus becomes extinct,under mild extra conditions,if R₀^S<1,the infected phytoplankton tend to go extinct;otherwise R₀^S>1,the infected phytoplankton is persistent in mean,mean-while,the solution of system is positive recurrence,which implies system admit a stationary distribution.