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Complex dynamics in a two species system with Crowley–Martin response function: Role of cooperation, additional food and seasonal perturbations

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  • Mondal, Bapin
  • Thirthar, Ashraf Adnan
  • Sk, Nazmul
  • Alqudah, Manar A.
  • Abdeljawad, Thabet

Abstract

This research article investigates the interaction between prey and a generalist predator, considering the effect of hunting cooperation. The predator–prey interaction is modeled using a predator dependent functional response, specifically the Crowley–Martin type. System’s dynamics are explored using both analytical and numerical techniques. Feasible equilibria are analyzed, and their local stability is determined. Various bifurcations in the system are explored, and one-and two-parameter bifurcation structures are constructed to unveil complex dynamical behaviors. Our findings reveal that both prey and predator face extinction when the predator growth rate from alternative food sources exceeds certain threshold values. However, prey extinction is driven by the higher levels of hunting cooperation among predators, while the availability of external food sources enhances the system’s stability and persistence. Furthermore, we enhance the model by introducing seasonal perturbations, acknowledging the influence of seasonal variations on ecological parameters. The system exhibits diverse patterns in response to seasonality, contributing to a deeper understanding of the dynamics in predator–prey interactions.

Suggested Citation

  • Mondal, Bapin & Thirthar, Ashraf Adnan & Sk, Nazmul & Alqudah, Manar A. & Abdeljawad, Thabet, 2024. "Complex dynamics in a two species system with Crowley–Martin response function: Role of cooperation, additional food and seasonal perturbations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 415-434.
    • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:415-434
    DOI: 10.1016/j.matcom.2024.03.015
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    References listed on IDEAS

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    1. 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.
    2. Sk, Nazmul & Tiwari, Pankaj Kumar & Pal, Samares, 2022. "A delay nonautonomous model for the impacts of fear and refuge in a three species food chain model with hunting cooperation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 136-166.
    3. Vagner Weide Rodrigues & Diomar Cristina Mistro & Luiz Alberto Díaz Rodrigues, 2019. "Pattern Formation and Bistability in a Generalist Predator-Prey Model," Mathematics, MDPI, vol. 8(1), pages 1-18, December.
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