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Journal of Applied Mathematics and Computing
Published in: Journal of Applied Mathematics and Computing 1-2/2021

07-01-2021 | Original Research

Bifurcations in a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten prey harvesting

Authors: Anuraj Singh, Pradeep Malik

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2021

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Abstract

In this paper, a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten type prey harvesting is investigated. It is shown that the model exhibits several bifurcations of codimension 1 viz. Neimark–Sacker bifurcation, transcritical bifurcation and flip bifurcation on varying one parameter. Bifurcation theory and center manifold theory are used to establish the conditions for the existence of these bifurcations. Moreover, existence of Bogdanov–Takens bifurcation of codimension 2 (i.e. two parameters must be varied for the occurrence of bifurcation) is exhibited. The non-degeneracy conditions are determined for occurrence of Bogdanov–Takens bifurcation. The extensive numerical simulation is performed to demonstrate the analytical findings. The system exhibits periodic solutions including flip bifurcation and Neimark–Sacker bifurcation followed by the wide range of dense chaos.
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Metadata
Title
Bifurcations in a modified Leslie–Gower predator–prey discrete model with Michaelis–Menten prey harvesting
Authors
Anuraj Singh
Pradeep Malik
Publication date
07-01-2021
Publisher
Springer Berlin Heidelberg
Published in
Journal of Applied Mathematics and Computing / Issue 1-2/2021
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-020-01491-9

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