Dynamical Behaviors Of The Nutrient-phytoplankton System In A Random Environment

In this paper,we focus on the dynamical behavior of the randomly disturbed nutrient-phytoplankton model,a simplified version of the nutrient-phytoplankton-zooplankton model based on the fact that phytoplankton such as algae have shorter growth cycles and zooplankton like fishes have longer growth cycles.This paper primarily applies certain techniques such as stochastic Lyapunov analysis,stochastic differential equations comparision theorem,strong ergodicity theorem.The general framework of this paper is as follows: Firstly,the existence and uniqueness of the global positive solution of the model are proved.Secondly,the stochastic final upper boundedness of phytoplankton and the stochastic persistence of nutrients are given.Next,the threshold of phytoplankton extinction and persistence in the stochastic model is studied: when < 0,the phytoplankton tend to extinction;when? > 0,the model exists an invariant measure and the random persistence of nutrients and phytoplankton is obtained,and then the mean persistence of nutrients and phytoplankton is explored.Finally,the obtained conclusions are further verified by giving two examples and performing numerical simulations.