IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v100y2017icp62-73.html
   My bibliography  Save this article

Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays

Author

Listed:
  • Shi, Renxiang
  • Yu, Jiang

Abstract

We take the delays due to gestation of two kinds of zooplankton as parameters, the dynamics of a two zooplankton-phytoplankton model is studied, we discussed the dynamics under six conditions: (1) τ1=τ2=0,(2) τ1>0,τ2=0, (3) τ1=0,τ2>0, (4) τ1=τ2>0, (5) τ1 ∈ (0, τ10), τ2 > 0, (6) τ2 ∈ (0, τ20), τ1 > 0, the Hopf bifurcation about condition (5) should be studied by center manifold theorem and normal form. At last, some simulations are given to support our results

Suggested Citation

  • Shi, Renxiang & Yu, Jiang, 2017. "Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 62-73.
    • Handle: RePEc:eee:chsofr:v:100:y:2017:i:c:p:62-73
    DOI: 10.1016/j.chaos.2017.04.044
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077917301790
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2017.04.044?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. Chakraborty, Subhendu & Roy, Shovonlal & Chattopadhyay, J., 2008. "Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: A mathematical model," Ecological Modelling, Elsevier, vol. 213(2), pages 191-201.
    2. Zhao, Jiantao & Wei, Junjie, 2009. "Stability and bifurcation in a two harmful phytoplankton–zooplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1395-1409.
    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. Zhao, Qiuyue & Liu, Shutang & Tian, Dadong, 2018. "Dynamic behavior analysis of phytoplankton–zooplankton system with cell size and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 160-168.
    2. Zhao, Qiuyue & Liu, Shutang & Niu, Xinglong, 2019. "Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 94-102.
    3. Barman, Binandita & Ghosh, Bapan, 2019. "Explicit impacts of harvesting in delayed predator-prey models," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 213-228.

    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. Jiang, Zhichao & Zhang, Tongqian, 2017. "Dynamical analysis of a reaction-diffusion phytoplankton-zooplankton system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 693-704.
    2. Li, Kai & Wei, Junjie, 2009. "Stability and Hopf bifurcation analysis of a prey–predator system with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2606-2613.
    3. 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).
    4. Raw, Sharada Nandan & Sahu, Sevak Ram, 2023. "Strong stability with impact of maturation delay and diffusion on a toxin producing phytoplankton–zooplankton model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 547-570.
    5. 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.
    6. 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).
    7. Poria, Swarup & Poria, Anindita Tarai & Chatterjee, Prasanta, 2009. "Synchronization threshold of a coupled n-dimensional time-delay system," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1123-1124.
    8. Grover, James P. & Roelke, Daniel L. & Brooks, Bryan W., 2012. "Modeling of plankton community dynamics characterized by algal toxicity and allelopathy: A focus on historical Prymnesium parvum blooms in a Texas reservoir," Ecological Modelling, Elsevier, vol. 227(C), pages 147-161.
    9. 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:100:y:2017:i:c:p:62-73. 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.