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Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling

Author

Listed:
  • Lifan Chen

    (School of Arts and Sciences, Shanghai University of Medicine and Health Sciences, Shanghai 201318, China)

  • Xingwang Yu

    (School of Management Engineering, Zhengzhou University of Aeronautics, Zhengzhou 450046, China)

  • Sanling Yuan

    (College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China)

Abstract

A stochastic nutrient–phytoplankton–zooplankton model with instantaneous nutrient recycling is proposed and analyzed in this paper. When the nutrient uptake function and the grazing function are linear and the ingested phytoplankton is completely absorbed by the zooplankton, we establish two stochastic thresholds R 0 S and R 1 S , which completely determine the persistence and extinction of the plankton. That is, if R 0 S < 1 , both the phytoplankton and the zooplankton eventually are eliminated; if R 0 S > 1 and R 1 S < 1 , the phytoplankton is persistent in mean but the zooplankton is extinct; while for R 1 S > 1 , the entire system is persistent in mean. Furthermore, sufficient criteria for the existence of ergodic stationary distribution of the model are obtained and the persistent levels of the plankton are estimated. Numeric simulations are carried out to illustrate the theoretical results and to conclude our study. Our results suggest that environmental noise may cause the local bloom of phytoplankton, which surprisingly can be used to explain the formation of algal blooms to some extent. Moreover, we find that the nonlinear nutrient uptake function and grazing function may take credit for the periodic succession of blooms regardless of whether they are in the absence or presence of the environmental noises.

Suggested Citation

  • Lifan Chen & Xingwang Yu & Sanling Yuan, 2022. "Effects of Random Environmental Perturbation on the Dynamics of a Nutrient–Phytoplankton–Zooplankton Model with Nutrient Recycling," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3783-:d:941706
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    References listed on IDEAS

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    1. Campillo, F. & Joannides, M. & Larramendy-Valverde, I., 2011. "Stochastic modeling of the chemostat," Ecological Modelling, Elsevier, vol. 222(15), pages 2676-2689.
    2. S. A. Amin & L. R. Hmelo & H. M. van Tol & B. P. Durham & L. T. Carlson & K. R. Heal & R. L. Morales & C. T. Berthiaume & M. S. Parker & B. Djunaedi & A. E. Ingalls & M. R. Parsek & M. A. Moran & E. V, 2015. "Interaction and signalling between a cosmopolitan phytoplankton and associated bacteria," Nature, Nature, vol. 522(7554), pages 98-101, June.
    3. Jang, Sophia R.-J. & Allen, Edward J., 2015. "Deterministic and stochastic nutrient-phytoplankton- zooplankton models with periodic toxin producing phytoplankton," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 52-67.
    4. Yu, Xingwang & Yuan, Sanling & Zhang, Tonghua, 2019. "Survival and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton in an impulsive polluted environment," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 249-264.
    5. Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
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