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Study of a Leslie–Gower predator-prey model with prey defense and mutual interference of predators

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  • Mishra, P.
  • Raw, S.N.
  • Tiwari, B.

Abstract

Prey can defend themselves against predators in many different ways. Some prey can even be dangerous to predators. Such prey posses morphological structures or behavioral adaptations, or release chemical substances that may lead to lower predation rate or death of predators. Motivated by this, we propose and analyze a predator-prey model to examine the central role of foraging in the lives of predators and dangerous prey. Three species model investigates complex dynamics in a predator-prey model that incorporates: (a) Prey defense; (b) mutual interference of predators; and (c) diffusion. We analyze boundedness of the proposed model and establish conditions for the existence of biologically feasible equilibrium points. The stability analysis of the proposed model is carried out. Conditions for Hopf bifurcation are obtained assuming growth of prey as bifurcation parameter. We analyze all the conditions for the occurrence of Turing instability in diffusion induced system. We perform numerical simulations to illustrate and justify our theoretical results. Our numerical simulation shows that proposed model has rich dynamics, including period halving and period doubling cascade. Effect of time delay on model dynamics is numerically studied. We observe some interesting complex patterns when parameter values are taken in Turing-Hopf domain. Finally, we conclude that better defense ability of prey is able to destabilize the predator-prey system.

Suggested Citation

  • Mishra, P. & Raw, S.N. & Tiwari, B., 2019. "Study of a Leslie–Gower predator-prey model with prey defense and mutual interference of predators," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 1-16.
    • Handle: RePEc:eee:chsofr:v:120:y:2019:i:c:p:1-16
    DOI: 10.1016/j.chaos.2019.01.012
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    References listed on IDEAS

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    1. Hu, Guang-Ping & Li, Wan-Tong & Yan, Xiang-Ping, 2009. "Hopf bifurcations in a predator–prey system with multiple delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1273-1285.
    2. Zizhen Zhang & Ranjit Kumar Upadhyay & Rashmi Agrawal & Jyotiska Datta, 2018. "The Gestation Delay: A Factor Causing Complex Dynamics in Gause-Type Competition Models," Complexity, Hindawi, vol. 2018, pages 1-21, November.
    3. Frank Hilker & Horst Malchow, 2006. "Strange Periodic Attractors in a Prey-Predator System with Infected Prey," Mathematical Population Studies, Taylor & Francis Journals, vol. 13(3), pages 119-134.
    4. Raw, S.N. & Mishra, P. & Kumar, R. & Thakur, S., 2017. "Complex behavior of prey-predator system exhibiting group defense: A mathematical modeling study," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 74-90.
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    Cited by:

    1. Parshad, Rana D. & Takyi, Eric M. & Kouachi, Said, 2019. "A remark on “Study of a Leslie-Gower predator-prey model with prey defense and mutual interference of predators” [Chaos, Solitons & Fractals 120 (2019) 1–16]," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 201-205.

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