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International Journal of Engineering Mathematics
Volume 2016 (2016), Article ID 2741891, 15 pages
Research Article

Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator

1Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow 226025, India
2Department of Mathematics, Faculty of Sciences, Banaras Hindu University, Varanasi 221605, India

Received 8 June 2016; Accepted 22 August 2016

Academic Editor: Krishnan Balachandran

Copyright © 2016 Manoj Kumar Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with the study of the stability and the bifurcation analysis of a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting. It is shown that the proposed model exhibits the bistability for certain parametric conditions. Dulac’s criterion has been adopted to obtain the sufficient conditions for the global stability of the model. Moreover, the model exhibits different kinds of bifurcations (e.g., the saddle-node bifurcation, the subcritical and supercritical Hopf bifurcations, Bogdanov-Takens bifurcation, and the homoclinic bifurcation) whenever the values of parameters of the model vary. The analytical findings and numerical simulations reveal far richer and complex dynamics in comparison to the models with no harvesting and with constant-yield predator harvesting.