IDEAS home Printed from https://ideas.repec.org/a/hin/complx/4590915.html
   My bibliography  Save this article

Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay

Author

Listed:
  • Kejun Zhuang
  • Gao Jia
  • Dezhi Liu

Abstract

Due to the different roles that nontoxic phytoplankton and toxin-producing phytoplankton play in the whole aquatic system, a delayed reaction-diffusion planktonic model under homogeneous Neumann boundary condition is investigated theoretically and numerically. This model describes the interactions between the zooplankton and two kinds of phytoplanktons. The long-time behavior of the model and existence of positive constant equilibrium solution are first discussed. Then, the stability of constant equilibrium solution and occurrence of Hopf bifurcation are detailed and analyzed by using the bifurcation theory. Moreover, the formulas for determining the bifurcation direction and stability of spatially bifurcating solutions are derived. Finally, some numerical simulations are performed to verify the appearance of the spatially homogeneous and nonhomogeneous periodic solutions.

Suggested Citation

  • Kejun Zhuang & Gao Jia & Dezhi Liu, 2019. "Stability and Hopf Bifurcation in a Three-Component Planktonic Model with Spatial Diffusion and Time Delay," Complexity, Hindawi, vol. 2019, pages 1-17, July.
    • Handle: RePEc:hin:complx:4590915
    DOI: 10.1155/2019/4590915
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/4590915.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/4590915.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/4590915?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
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Pal, S. & Chatterjee, Samrat & Das, Krishna pada & Chattopadhyay, J., 2009. "Role of competition in phytoplankton population for the occurrence and control of plankton bloom in the presence of environmental fluctuations," Ecological Modelling, Elsevier, vol. 220(2), pages 96-110.
    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. 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.

    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. Mondal, Chirodeep & Kesh, Dipak & Mukherjee, Debasis, 2023. "Global stability and bifurcation analysis of an infochemical induced three species discrete-time phytoplankton–zooplankton model," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Gökçe, Aytül & Yazar, Samire & Sekerci, Yadigar, 2020. "Delay induced nonlinear dynamics of oxygen-plankton interactions," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. 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.
    4. Ghorai, Santu & Poria, Swarup, 2016. "Pattern formation and control of spatiotemporal chaos in a reaction diffusion prey–predator system supplying additional food," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 57-67.
    5. Zheng, Yanlin & Gong, Xiang & Gao, Huiwang, 2022. "Selective grazing of zooplankton on phytoplankton defines rapid algal succession and blooms in oceans," Ecological Modelling, Elsevier, vol. 468(C).
    6. Chen, Zhewen & Tian, Zhuyan & Zhang, Shuwen & Wei, Chunjin, 2020. "The stationary distribution and ergodicity of a stochastic phytoplankton–zooplankton model with toxin-producing phytoplankton under regime switching," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    7. 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.
    8. Animesh Mahata & Sankar Prasad Mondal & Banamali Roy & Shariful Alam, 2021. "Study of two species prey-predator model in imprecise environment with MSY policy under different harvesting scenario," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(10), pages 14908-14932, October.

    More about this item

    Statistics

    Access and download statistics

    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:hin:complx:4590915. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.