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Computational Ecology and Software, 2019, 9(3): 67-88
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Article

Chaotic behavior of harvesting Leslie-Gower predator-prey model

Muhammad Asif Khan1, Muhammad Sajjad Shabbir2, Qamar Din1, Khalil Ahmad2
1Department of Mathematics, The University of PoonchRawalakot, Rawalakot 12350, Pakistan
2Department of Mathematics, Air University Islamabad, 44230, Pakistan

Received 19 March 2019;Accepted 20 April 2019;Published 1 September 2019
IAEES

Abstract
This article deals with the study of some qualitative properties of a harvesting Leslie-Gower predator-prey model. Particularly, we explore the existence, uniqueness, boundedness of positive equilibrium point and local stability analysis of positive equilibrium point. Moreover, it is shown that there exists period-doubling bifurcation and Nimark-sacker bifurcation for the unique positive steady-state of given system. In order to control the bifurcation we introduce a feedback strategy. For further confirmation of complexity and chaotic behavior largest Lyapunov exponents are plotted.

Keywords predator-prey model;period-doubling bifurcation;Nimark-Sacker bifurcation;chaos control.


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