IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v104y2017icp389-399.html
   My bibliography  Save this article

Effects of toxicants on Phytoplankton-Zooplankton-Fish dynamics and harvesting

Author

Listed:
  • Panja, Prabir
  • Mondal, Shyamal Kumar
  • Jana, Dipak Kumar

Abstract

In this paper, a three species predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed in the presence of toxicant. It is assumed that Phytoplankton grows logistically and its growth rate is affected by toxin release in the environment through different natural and human activities. It is considered that Zooplankton consumes only Phytoplankton. Fish consumes both Phytoplankton as well as Zooplankton. Here, it is also assume that Phytoplankton releases some toxin in the environment which makes some death on Zooplankton. Also, it is considered that toxicant in the environment are increased constantly for different natural and human behavior. Then, different equilibrium points have been determined and the stability of the proposed system has been analyzed around these equilibrium points. Hopf bifurcation analysis has been done with respect to the contact rate between Phytoplankton and Environmental toxin (γ), constant rate of increase of Environmental toxin (A) , depletion rate of environmental toxin (d1), harvesting effort (E) and rate of releasing toxin by Phytoplankton (ρ). From this study, it is seen that these parameters have a big role on the stability of this predator prey system. Finally, some numerical simulation results have been shown to verify our analytical findings.

Suggested Citation

  • Panja, Prabir & Mondal, Shyamal Kumar & Jana, Dipak Kumar, 2017. "Effects of toxicants on Phytoplankton-Zooplankton-Fish dynamics and harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 389-399.
    • Handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:389-399
    DOI: 10.1016/j.chaos.2017.08.036
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917303533
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.08.036?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Das, Kalyan & Ray, Santanu, 2008. "Effect of delay on nutrient cycling in phytoplankton–zooplankton interactions in estuarine system," Ecological Modelling, Elsevier, vol. 215(1), pages 69-76.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hossain, Mainul & Pati, N.C. & Pal, Saheb & Rana, Sourav & Pal, Nikhil & Layek, G.C., 2021. "Bifurcations and multistability in a food chain model with nanoparticles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 808-825.
    2. Renu, & Upadhyay, Ranjit Kumar & Tiwari, S.P. & Yadav, R.P., 2023. "Analysis of interval-valued model for interaction between plankton-fish population in marine ecosystem," Ecological Modelling, Elsevier, vol. 484(C).
    3. Sk Golam Mortoja & Prabir Panja & Shyamal Kumar Mondal, 2023. "Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish," Mathematics, MDPI, vol. 11(13), pages 1-37, July.
    4. Sajan, & Kumar Choudhary, Kapil & Dubey, Balram, 2023. "A non-autonomous approach to study the impact of environmental toxins on nutrient-plankton system," Applied Mathematics and Computation, Elsevier, vol. 458(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Thakur, Nilesh Kumar & Ojha, Archana & Tiwari, Pankaj Kumar & Upadhyay, Ranjit Kumar, 2021. "An investigation of delay induced stability transition in nutrient-plankton systems," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Chuanjun Dai & Hengguo Yu & Qing Guo & He Liu & Qi Wang & Zengling Ma & Min Zhao, 2019. "Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-16, February.
    3. Renu, & Upadhyay, Ranjit Kumar & Tiwari, S.P. & Yadav, R.P., 2023. "Analysis of interval-valued model for interaction between plankton-fish population in marine ecosystem," Ecological Modelling, Elsevier, vol. 484(C).
    4. Agnihotri, Kulbhushan & Kaur, Harpreet, 2019. "The dynamics of viral infection in toxin producing phytoplankton and zooplankton system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 122-133.
    5. 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).
    6. Zhang, Jia-Fang & Wang, Shaoli & Kong, Xiangjun, 2018. "Effects of toxin delay on the dynamics of a phytoplankton–zooplankton model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1150-1162.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:104:y:2017:i:c:p:389-399. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.