IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v190y2021icp808-825.html
   My bibliography  Save this article

Bifurcations and multistability in a food chain model with nanoparticles

Author

Listed:
  • Hossain, Mainul
  • Pati, N.C.
  • Pal, Saheb
  • Rana, Sourav
  • Pal, Nikhil
  • Layek, G.C.

Abstract

In the present paper, we report the effect of nanoparticles in a three-species aquatic food chain model. It is assumed that due to the unavoidable interactions with nanoparticles, the growth rate of basal prey reduces. Fascinating dynamical scenarios in the model are explored in different bi-parametric spaces. We show that the model exhibits coexisting attractors of different kinds (periodic–periodic/periodic–chaotic) in some regions of the bi-parametric space. We also discover well-organized shrimp-shaped periodic structures in the chaotic regime, indicating the coexistence of order (regular pattern) and chaos. Further, a period-bubbling transition to chaos is found near the inner boundaries of the shrimp-shaped structure. It is also observed that managing the depletion rate of the nanoparticles can be used as a control strategy to prevent population extinction in an aquatic food chain system.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:808-825
    DOI: 10.1016/j.matcom.2021.06.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421002408
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.06.017?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. Pati, N.C. & Layek, G.C. & Pal, Nikhil, 2020. "Bifurcations and organized structures in a predator-prey model with hunting cooperation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. 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.
    3. Pal, Nikhil & Samanta, Sudip & Chattopadhyay, Joydev, 2014. "Revisited Hastings and Powell model with omnivory and predator switching," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 58-73.
    4. Andrew D. Maynard & Robert J. Aitken & Tilman Butz & Vicki Colvin & Ken Donaldson & Günter Oberdörster & Martin A. Philbert & John Ryan & Anthony Seaton & Vicki Stone & Sally S. Tinkle & Lang Tran & N, 2006. "Safe handling of nanotechnology," Nature, Nature, vol. 444(7117), pages 267-269, November.
    5. Sahoo, Banshidhar & Poria, Swarup, 2014. "The chaos and control of a food chain model supplying additional food to top-predator," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 52-64.
    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. Rashi, & Singh, Harendra Pal & Singh, Suruchi, 2024. "Effect of fear with saturated fear cost and harvesting on aquatic food chain model (plankton–fish model) in the presence of nanoparticles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 283-305.
    2. Garai, Shilpa & Pati, N.C. & Pal, Nikhil & Layek, G.C., 2022. "Organized periodic structures and coexistence of triple attractors in a predator–prey model with fear and refuge," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Hossain, Mainul & Kumbhakar, Ruma & Pal, Nikhil, 2022. "Dynamics in the biparametric spaces of a three-species food chain model with vigilance," Chaos, Solitons & Fractals, Elsevier, vol. 162(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. Wang, Jin-Shan & Wu, Yong-Ping & Li, Li & Sun, Gui-Quan, 2020. "Effect of mobility and predator switching on the dynamical behavior of a predator-prey model," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. 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).
    3. Tian, Yuan & Li, Huanmeng & Sun, Kaibiao, 2024. "Complex dynamics of a fishery model: Impact of the triple effects of fear, cooperative hunting and intermittent harvesting," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 31-48.
    4. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    5. Thirthar, Ashraf Adnan & Majeed, Salam J. & Alqudah, Manar A. & Panja, Prabir & Abdeljawad, Thabet, 2022. "Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. N. C. Pati, 2023. "Bifurcations and multistability in a physically extended Lorenz system for rotating convection," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-15, August.
    7. Nikhil Pal & Sudip Samanta & Maia Martcheva & Joydev Chattopadhyay, 2018. "Role of Bi-Directional Migration in Two Similar Types of Ecosystems," Mathematics, MDPI, vol. 6(3), pages 1-16, March.
    8. Douglas J. Sylvester & Kenneth W. Abbott & Gary E. Marchant, 2009. "Not again! Public perception, regulation, and nanotechnology," Regulation & Governance, John Wiley & Sons, vol. 3(2), pages 165-185, June.
    9. Uddin, Md. Jasim & Rana, Sarker Md. Sohel & Işık, Seval & Kangalgil, Figen, 2023. "On the qualitative study of a discrete fractional order prey–predator model with the effects of harvesting on predator population," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    10. Vishwakarma, Krishnanand & Sen, Moitri, 2021. "Role of Allee effect in prey and hunting cooperation in a generalist predator," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 622-640.
    11. Pandey, Soumik & Ghosh, Uttam & Das, Debashis & Chakraborty, Sarbani & Sarkar, Abhijit, 2024. "Rich dynamics of a delay-induced stage-structure prey–predator model with cooperative behaviour in both species and the impact of prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 216(C), pages 49-76.
    12. 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.
    13. 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.
    14. Chou, Yen-hsi & Chow, Yunshyong & Hu, Xiaochuan & Jang, Sophia R.-J., 2021. "A Ricker–type predator–prey system with hunting cooperation in discrete time," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 570-586.
    15. Drubi, Fátima & Ibáñez, Santiago & Pilarczyk, Paweł, 2021. "Nilpotent singularities and chaos: Tritrophic food chains," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    16. Sahoo, Banshidhar & Poria, Swarup, 2015. "Effects of allochthonous inputs in the control of infectious disease of prey," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 1-19.
    17. Kaur, Rajinder Pal & Sharma, Amit & Sharma, Anuj Kumar & Sahu, Govind Prasad, 2021. "Chaos control of chaotic plankton dynamics in the presence of additional food, seasonality, and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    18. Liu, Chao & Xun, Xinying & Zhang, Guilai & Li, Yuanke, 2020. "Stochastic dynamics and optimal control in a hybrid bioeconomic system with telephone noise and Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    19. Yanfei Du & Ben Niu & Junjie Wei, 2021. "Dynamics in a Predator–Prey Model with Cooperative Hunting and Allee Effect," Mathematics, MDPI, vol. 9(24), pages 1-40, December.
    20. Lubna Noor & Bakhtawar Sajjad, 2020. "Synthesis of NiO/ZnO Nanoparticles using 2-Propanol Solvent and their Applications for Methylene Blue Degradation," International Journal of Innovations in Science & Technology, 50sea, vol. 2(2), pages 38-45, March.

    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:matcom:v:190:y:2021:i:c:p:808-825. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.