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A remark on “Study of a Leslie–Gower-type tritrophic population model” [Chaos, Solitons and Fractals 14 (2002) 1275–1293]

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  • Parshad, Rana D.
  • Kumari, Nitu
  • Kouachi, Said

Abstract

In Aziz-Alaoui (2002) a three species ODE model, based on a modified Leslie–Gower scheme is investigated. It is shown that under certain restrictions on the parameter space, the model has bounded solutions for all positive initial conditions, which eventually enter an invariant attracting set. We show that this is not true. To the contrary, solutions to the model can blow up in finite time, even under the restrictions derived in Aziz-Alaoui (2002), if the initial data is large enough. We also prove similar results for the spatially extended system. We validate all of our results via numerical simulations.

Suggested Citation

  • Parshad, Rana D. & Kumari, Nitu & Kouachi, Said, 2015. "A remark on “Study of a Leslie–Gower-type tritrophic population model” [Chaos, Solitons and Fractals 14 (2002) 1275–1293]," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 22-28.
    • Handle: RePEc:eee:chsofr:v:71:y:2015:i:c:p:22-28
    DOI: 10.1016/j.chaos.2014.11.014
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    References listed on IDEAS

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    1. Gakkhar, Sunita & Singh, Brahampal, 2005. "Complex dynamic behavior in a food web consisting of two preys and a predator," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 789-801.
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    Cited by:

    1. Quansah, Emmanuel & Parshad, Rana D. & Mondal, Sumona, 2017. "Cold induced mortality of the Burmese Python: An explanation via stochastic analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 356-364.
    2. 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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