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The chaos and control of a food chain model supplying additional food to top-predator

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  • Sahoo, Banshidhar
  • Poria, Swarup

Abstract

The control and management of chaotic population is one of the main objectives for constructing mathematical model in ecology today. In this paper, we apply a technique of controlling chaotic predator–prey population dynamics by supplying additional food to top-predator. We formulate a three species predator–prey model supplying additional food to top-predator. Existence conditions and local stability criteria of equilibrium points are determined analytically. Persistence conditions for the system are derived. Global stability conditions of interior equilibrium point is calculated. Theoretical results are verified through numerical simulations. Phase diagram is presented for various quality and quantity of additional food. One parameter bifurcation analysis is done with respect to quality and quantity of additional food separately keeping one of them fixed. Using MATCONT package, we derive the bifurcation scenarios when both the parameters quality and quantity of additional food vary together. We predict the existence of Hopf point (H), limit point (LP) and branch point (BP) in the model for suitable supply of additional food. We have computed the regions of different dynamical behaviour in the quantity–quality parametric plane. From our study we conclude that chaotic population dynamics of predator prey system can be controlled to obtain regular population dynamics only by supplying additional food to top predator. This study is aimed to introduce a new non-chemical chaos control mechanism in a predator–prey system with the applications in fishery management and biological conservation of prey predator species.

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  • 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.
    • Handle: RePEc:eee:chsofr:v:58:y:2014:i:c:p:52-64
    DOI: 10.1016/j.chaos.2013.11.008
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    References listed on IDEAS

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    1. El-Gohary, Awad & Al-Ruzaiza, A.S., 2007. "Chaos and adaptive control in two prey, one predator system with nonlinear feedback," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 443-453.
    2. Wang, Fengyan & Zeng, Guangzhao, 2007. "Chaos in a Lotka–Volterra predator–prey system with periodically impulsive ratio-harvesting the prey and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1499-1512.
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    Cited by:

    1. Saikia, Munmi & Maiti, Atasi Patra & Devi, Anuradha, 2020. "Effect of habitat complexity on rhinoceros and tiger population model with additional food and poaching in Kaziranga National Park, Assam," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 169-191.
    2. Drubi, Fátima & Ibáñez, Santiago & Pilarczyk, Paweł, 2021. "Nilpotent singularities and chaos: Tritrophic food chains," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. 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.
    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. 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.
    6. 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).
    7. 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.
    8. 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).
    9. 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).
    10. Ghosh, Joydev & Sahoo, Banshidhar & Poria, Swarup, 2017. "Prey-predator dynamics with prey refuge providing additional food to predator," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 110-119.
    11. Iqbal, Muhammad & Rehan, Muhammad & Hong, Keum-Shik & Khaliq, Abdul & Saeed-ur-Rehman,, 2015. "Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 158-169.

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