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Deterministic and stochastic nutrient-phytoplankton- zooplankton models with periodic toxin producing phytoplankton

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  • Jang, Sophia R.-J.
  • Allen, Edward J.

Abstract

Deterministic and stochastic models of nutrient-phytoplankton-zooplankton interaction are proposed to investigate the impact of toxin producing phytoplankton upon persistence of the populations. The toxin liberation by phytoplankton is modeled periodically in the deterministic system. We derive two thresholds in terms of the parameters for which both plankton populations can persist if these thresholds are positive. We construct stochastic models with Itô differential equations to model variability in the environment. It is concluded that the input nutrient concentration along with the toxin liberation rate play critical roles in the dynamics of the planktonic interaction. In particular, toxin producing phytoplankton can terminate harmful algal blooms and the planktonic interaction is more stable if either the input nutrient concentration is smaller or if the toxin production rate is larger.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:52-67
    DOI: 10.1016/j.amc.2015.08.065
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    Citations

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    Cited by:

    1. Guo, Qing & Wang, Yi & Dai, Chuanjun & Wang, Lijun & Liu, He & Li, Jianbing & Tiwari, Pankaj Kumar & Zhao, Min, 2023. "Dynamics of a stochastic nutrient–plankton model with regime switching," Ecological Modelling, Elsevier, vol. 477(C).
    2. Liu, He & Dai, Chuanjun & Yu, Hengguo & Guo, Qing & Li, Jianbing & Hao, Aimin & Kikuchi, Jun & Zhao, Min, 2023. "Dynamics of a stochastic non-autonomous phytoplankton–zooplankton system involving toxin-producing phytoplankton and impulsive perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 368-386.
    3. Yuanlin Ma & Xingwang Yu, 2022. "Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    4. Zhao, Shengnan & Yuan, Sanling & Zhang, Tonghua, 2022. "The impact of environmental fluctuations on a plankton model with toxin-producing phytoplankton and patchy agglomeration," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    5. 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.
    6. Liao, Tiancai, 2022. "The impact of plankton body size on phytoplankton-zooplankton dynamics in the absence and presence of stochastic environmental fluctuation," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    7. Soukaina, Ben Rhila & Imane, Agmour & Mostafa, Rachik & Naceur, Achtaich & Youssef, El Foutayeni, 2022. "Optimal control of a phytoplankton-zooplankton spatiotemporal discrete bioeconomic model," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    8. Xiaomei Feng & Yuan Miao & Shulin Sun & Lei Wang, 2022. "Dynamic Behaviors of a Stochastic Eco-Epidemiological Model for Viral Infection in the Toxin-Producing Phytoplankton and Zooplankton System," Mathematics, MDPI, vol. 10(8), pages 1-18, April.
    9. Gao, Miaomiao & Jiang, Daqing & Ding, Jieyu, 2023. "Dynamical behavior of a nutrient–plankton model with Ornstein–Uhlenbeck process and nutrient recycling," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    10. Chakraborty, Subhendu & Moorthi, Stefanie D. & Karnatak, Rajat & Feudel, Ulrike, 2022. "Irregular harmful algal blooms triggered by feedback between toxin production and zooplankton feeding," Ecological Modelling, Elsevier, vol. 473(C).
    11. Das, Tanaya & Chakraborti, Saranya & Mukherjee, Joydeep & Sen, Goutam Kumar, 2018. "Mathematical modelling for phytoplankton distribution in Sundarbans Estuarine System, India," Ecological Modelling, Elsevier, vol. 368(C), pages 111-120.
    12. Sun, Shulin & Sun, Yaru & Zhang, Guang & Liu, Xinzhi, 2017. "Dynamical behavior of a stochastic two-species Monod competition chemostat model," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 153-170.

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