In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects...In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invari- ant and asymptotically stable density. Numerical simulations illustrate our theoretical results.展开更多
基金This research is supported by the National Natural Science Foundation of China （11271260）, Innovation Program of Shanghai Municipal Education Committee （13ZZ116）, Shanghai Leading Academic Discipline Project （XTKX2012）, Hujiang Foundation of China （B14005） and China Scholarship Council.
文摘In this paper, the dynamics of a stochastic model for algal bloom with nutrient recy- cling is investigated. The model incorporates a white noise term in the growth equation of algae population to describe the effects of random fluctuations in the environment, and a nutrient recycling term in the nutrient equation to account for the conversion of detritus into nutrient. The existence and uniqueness of the global positive solution of the model is first proved. Then we study the long-time behavior of the model. Conditions for the extinction and persistence in the mean of the algae population are established. By using the theory of integral Markov semigroups, we show that the model has an invari- ant and asymptotically stable density. Numerical simulations illustrate our theoretical results.
