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Role of fear in predator–prey system with intraspecific competition

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  • Mukherjee, Debasis

Abstract

Predator–prey interaction is considered as a natural phenomenon in ecological system. An obvious question arises in ecosystem is that how predator affect the density of prey population. In most of the ecological models, predators reduce prey densities by direct killing which is a minor part in population dynamics. Experimental studies on vertebrate has shown that fear of predators can influence the behavioural pattern of prey population and reduce their reproduction. Mathematical models of predator–prey system with variety of predator functional responses with fear effect are studied recently. These studies ignore the fear effect on the death rate of prey species. Based on the above observation, we propose a mathematical model of predator–prey system with the cost of fear that affect reproduction and death rate of prey population. We also include a term modelling intraspecific competition within the predator population. This additional term limits the predator population growth for large predator to prey density ratios. Basic results on the positivity and boundedness of the solutions, feasibility of equilibria, local and global stability and uniform persistence (ensuring the long term survival of the species) and limit cycles and its nature are investigated. Numerical experiments are performed to test the theoretical results obtained for this model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:263-275
    DOI: 10.1016/j.matcom.2020.04.025
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. 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).
    2. Liang, Ziwei & Meng, Xinyou, 2023. "Stability and Hopf bifurcation of a multiple delayed predator–prey system with fear effect, prey refuge and Crowley–Martin function," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    3. 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.
    4. Das, Bijoy Kumar & Sahoo, Debgopal & Samanta, G.P., 2022. "Impact of fear in a delay-induced predator–prey system with intraspecific competition within predator species," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 134-156.

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