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Impact of adult predator incited fear in a stage-structured prey–predator model

Author

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  • Narayan Mondal

    (Indian Institute of Engineering Science and Technology, Shibpur)

  • Dipesh Barman

    (Indian Institute of Engineering Science and Technology, Shibpur)

  • Shariful Alam

    (Indian Institute of Engineering Science and Technology, Shibpur)

Abstract

A two-species predator–prey model where the predators are separated into juvenile and mature predators has been considered in this article. Here, functional response in linear form is considered to know the impact of adult predator-induced fear in the stage-structured prey–predator model. Positivity and boundedness of the model system have been checked. Persistence conditions and existence condition(s) of each equilibria have been derived. The local and global stability analysis have been implemented both analytically and numerically along with Hopf bifurcation analysis with direction. From the analysis of the model system, it is observed that the mature predator-induced fear and rate of transition from juvenile (minor) predator to mature predator plays a crucial role in controlling the system dynamics.

Suggested Citation

  • Narayan Mondal & Dipesh Barman & Shariful Alam, 2021. "Impact of adult predator incited fear in a stage-structured prey–predator model," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(6), pages 9280-9307, June.
    • Handle: RePEc:spr:endesu:v:23:y:2021:i:6:d:10.1007_s10668-020-01024-1
    DOI: 10.1007/s10668-020-01024-1
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    References listed on IDEAS

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    1. Meng, Xin-You & Huo, Hai-Feng & Xiang, Hong & Yin, Qi-yu, 2014. "Stability in a predator–prey model with Crowley–Martin function and stage structure for prey," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 810-819.
    2. Kundu, Soumen & Maitra, Sarit, 2018. "Dynamics of a delayed predator-prey system with stage structure and cooperation for preys," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 453-460.
    3. Lu, Yang & Pawelek, Kasia A. & Liu, Shengqiang, 2017. "A stage-structured predator-prey model with predation over juvenile prey," Applied Mathematics and Computation, Elsevier, vol. 297(C), pages 115-130.
    4. 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.
    5. Khajanchi, Subhas, 2017. "Modeling the dynamics of stage-structure predator-prey system with Monod–Haldane type response function," Applied Mathematics and Computation, Elsevier, vol. 302(C), pages 122-143.
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