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Fear effect in a predator-prey model with additional food, prey refuge and harvesting on super predator

Author

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  • Thirthar, Ashraf Adnan
  • Majeed, Salam J.
  • Alqudah, Manar A.
  • Panja, Prabir
  • Abdeljawad, Thabet

Abstract

The shape of the interaction between three species: prey, predator, and super predator has been considered in this work as a new predator-prey model. In this article, the fear of predator in prey species has been introduced. Also, we have considered that the predation of both prey and predator occurs according to the Beddington-DeAngelis type functional response. The predator is thought to be acting as a shelter for the super predator species. It is anticipated that a constant amount of increased food will be delivered to super predators due to their dread of predators and their refuge behavior, and that predators will benefit from this excess food. The non-negativity and boundedness of solutions of the prosed model have been examined. The system's local and global stability at the interior equilibrium points has been explored. The existence condition of Hopf bifurcation of the system with respect to fear f of predator has been studied. From the analysis of the model, it is found that the fear f of predator may be responsible for the system's stability. It's also been discovered that providing extra food to the super predator may help to keep the system in check. Further, it is found that the refuge of predator to the super predator has the ability to stabilize the predator-prey system. Finally, some intriguing numerical simulation findings were provided in order to study the model's dynamics.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003010
    DOI: 10.1016/j.chaos.2022.112091
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    References listed on IDEAS

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    1. Evan L Preisser & Daniel I Bolnick, 2008. "The Many Faces of Fear: Comparing the Pathways and Impacts of Nonconsumptive Predator Effects on Prey Populations," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-8, June.
    2. 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.
    3. 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.
    4. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
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    Cited by:

    1. Shivam, & Singh, Kuldeep & Kumar, Mukesh & Dubey, Ramu & Singh, Teekam, 2022. "Untangling role of cooperative hunting among predators and herd behavior in prey with a dynamical systems approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Seralan Vinoth & R. Vadivel & Nien-Tsu Hu & Chin-Sheng Chen & Nallappan Gunasekaran, 2023. "Bifurcation Analysis in a Harvested Modified Leslie–Gower Model Incorporated with the Fear Factor and Prey Refuge," Mathematics, MDPI, vol. 11(14), pages 1-25, July.
    3. Arjun Hasibuan & Asep Kuswandi Supriatna & Endang Rusyaman & Md. Haider Ali Biswas, 2023. "Predator–Prey Model Considering Implicit Marine Reserved Area and Linear Function of Critical Biomass Level," Mathematics, MDPI, vol. 11(18), pages 1-16, September.

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