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Bifurcations and multistability in a food chain model with nanoparticles

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Pal, Saheb & Pal, Nikhil, 2025. "Modelling the wind effect in predator–prey interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 75-90.
    2. 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.
    3. 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).
    4. 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).

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