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Qualitative Analysis of an Additional Food Provided Predator–Prey Model in the Presence of Allee Effect

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Abstract

The present paper analyzes a predator–prey model in which the predator is provided with additional food and subjected to Allee effect. The conditions for the existence of equilibrium points and their local stability have been investigated. Under certain conditions, it is found that the solutions depend highly on the initial values. The existence of the bifurcations such as Bogdanov–Takens, Hopf–Andronov, Transcritical and Saddle-node, for the system have been shown. Further, the appearance of homoclinic loop, emerging through Hopf-bifurcation has been shown through numerical simulation. Numerical simulations have been proposed to confirm the analytical results.

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Acknowledgements

The author Manoj Kumar Singh gratefully acknowledges the financial assistance from Babasaheb Bhimrao Ambedkar University, Lucknow, India as a research fellowship.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Banasthali University, Rajasthan, 304022, India

    Manoj Kumar Singh

  2. Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, 226025, India

    B. S. Bhadauria

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Correspondence to B. S. Bhadauria.

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On behalf of the co-author, I hereby declare that we do not have any conflict of interest in publishing the manuscript of the paper entitled “Qualitative analysis of an additional food provided predator–prey model in the presence of Allee-effect” by Manoj Kumar Singh and B.S. Bhadauria in International Journal of Applied and Computational Mathematics.

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Singh, M.K., Bhadauria, B.S. Qualitative Analysis of an Additional Food Provided Predator–Prey Model in the Presence of Allee Effect. Int. J. Appl. Comput. Math 3 (Suppl 1), 1173–1195 (2017). https://doi.org/10.1007/s40819-017-0409-2

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