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

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 sh...

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Published in:Chaos, solitons and fractals solitons and fractals, 2015-02, Vol.71, p.22-28
Main Authors: Parshad, Rana D., Kumari, Nitu, Kouachi, Said
Format: Article
Language:English
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Summary: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.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2014.11.014