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Analysis of a stochastic model for algal bloom with nutrient recycling. (English) Zbl 1346.92057

Summary: In this paper, the dynamics of a stochastic model for algal bloom with nutrient recycling 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 invariant and asymptotically stable density. Numerical simulations illustrate our theoretical results.

MSC:

92D25 Population dynamics (general)
65C20 Probabilistic models, generic numerical methods in probability and statistics
65C30 Numerical solutions to stochastic differential and integral equations
92D40 Ecology
47D07 Markov semigroups and applications to diffusion processes
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