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Effects of fear in a fractional-order predator-prey system with predator density-dependent prey mortality

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  • Yousef, Fatma Bozkurt
  • Yousef, Ali
  • Maji, Chandan

Abstract

In this work, we have formulated a fractional-order predator-prey system with fear effect, where the death rate of the prey population is predator density-dependent. Generally, most of the ecological study considers the direct killing of prey in a predator’s presence, but they ignore the effect of predators’ presence on prey. Some experimental studies confirmed that fear affects the reproduction rate of the prey population, but a few studies are there, which conclude that fear also affects the death rate of the prey population. Thus our main aim in this work is to investigate the influence of the fear effect produced by a predator on the reproduction rate and death rate of the prey population. We first prove the existence, uniqueness, non-negativity, and boundedness of the considered model solutions. After that, we show a detailed analysis of different equilibria and their stability criteria based on some conditions where we specifically investigated the global stability of the interior equilibrium point. Besides that, the existence of Hopf bifurcation and the persistence of the system is derived. We also observed how fractional-order derivative also has an impact on our proposed system. Finally, some numerical simulation is performed to validate our findings.

Suggested Citation

  • Yousef, Fatma Bozkurt & Yousef, Ali & Maji, Chandan, 2021. "Effects of fear in a fractional-order predator-prey system with predator density-dependent prey mortality," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921000643
    DOI: 10.1016/j.chaos.2021.110711
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Singh, Brahampal, 2007. "The dynamics of a food web consisting of two preys and a harvesting predator," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1346-1356.
    2. Zhang, Huisen & Cai, Yongli & Fu, Shengmao & Wang, Weiming, 2019. "Impact of the fear effect in a prey-predator model incorporating a prey refuge," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 328-337.
    3. Ji, Guilin & Ge, Qing & Xu, Jiabo, 2016. "Dynamic behaviors of a fractional order two-species cooperative systems with harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 51-55.
    4. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    5. 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.
    6. Mukherjee, Debasis, 2020. "Role of fear in predator–prey system with intraspecific competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 263-275.
    7. Nosrati, Komeil & Shafiee, Masoud, 2017. "Dynamic analysis of fractional-order singular Holling type-II predator–prey system," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 159-179.
    8. Moustafa, Mahmoud & Mohd, Mohd Hafiz & Ismail, Ahmad Izani & Abdullah, Farah Aini, 2018. "Dynamical analysis of a fractional-order Rosenzweig–MacArthur model incorporating a prey refuge," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 1-13.
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    Cited by:

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    3. 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).
    4. Pal, Debjit & Kesh, Dipak & Mukherjee, Debasis, 2024. "Cross-diffusion mediated Spatiotemporal patterns in a predator–prey system with hunting cooperation and fear effect," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 128-147.
    5. Zhang, Hai & Cheng, Jingshun & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2021. "Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Zhang, Hai & Cheng, Yuhong & Zhang, Weiwei & Zhang, Hongmei, 2023. "Time-dependent and Caputo derivative order-dependent quasi-uniform synchronization on fuzzy neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 846-857.

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