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Stochastic dynamics of a plankton model with zooplankton selectivity and nutritional value of phytoplankton

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Abstract

In this paper, we study the stochastic dynamics of a preferred phytoplankton (PP)–nonpreferred phytoplankton (NP)–zooplankton (Z) model with selectivity of zooplankton and nutritional value of phytoplankton. The mathematical theoretical work mainly gives the existence and uniqueness of the positive solution, provides the results related to stochastic ultimate boundedness and stochastic permanence, shows the dynamics of stochastic extinction and persistence in the mean, and proves the existence of a unique ergodic stationary distribution, which in turn provides a theoretical basis for numerical simulations. The numerical simulation work mainly reveals that the selectivity of zooplankton and nutritional of phytoplankton have a significant impact on the PP–NP–Z dynamics under random environmental fluctuation. It is worth emphasizing that the large nutritional value of preferred phytoplankton has the capacity to result in the extinction of nonpreferred phytoplankton, while the large nutritional value of nonpreferred phytoplankton may be able to initiate the occurrence of harmful algal blooms. Furthermore, it should be noted that the increase of zooplankton selectivity or nutritional value of phytoplankton (preferred phytoplankton and nonpreferred phytoplankton) can cause the stationary distribution of preferred phytoplankton to shift to the left, but the stationary distribution of nonpreferred phytoplankton and zooplankton can shift to the right. These results may contribute to further understanding the complex dynamics of plankton models.

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Acknowledgements

This research was supported by Natural Science Foundation Project of Jiangsu Provincial Department of Education, Jiangsu Province, China(21KJD110005).

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  1. School of Mathematics and Statistics, Huaiyin Normal University, Huaian, 223300, Jiangsu, People’s Republic of China

    Tiancai Liao

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Liao, T. Stochastic dynamics of a plankton model with zooplankton selectivity and nutritional value of phytoplankton. J. Appl. Math. Comput. 70, 251–283 (2024). https://doi.org/10.1007/s12190-023-01959-4

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