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Network Biology, 2019, 9(3): 58-77
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Article

Stability, bifurcation and chaos control in a discrete-time prey-predator model with Holling type-II response

Muhammad Salman Khan1, Muhammad Asif Khan2, Muhammad Sajjad Shabbir3, Qamar Din2
1Department of Mathematics, Quaid-I-Azam University Islamabad, 44230, Pakistan
2Department of Mathematics, University of the PoonchRawalakot, Rawalakot 12350, Pakistan
3Department of Mathematics, Air University Islamabad, 44230, Pakistan

Received 11 May 2019;Accepted 10 June 2019;Published 1 September 2019
IAEES

Abstract
This paper deals with the qualitative study of a discrete-time prey-predator model with Holling type-II response. Particularly, we obtained a dynamically consistent prey-predator discrete-time model by applying a nonstandard difference scheme. We explore the novel explicate parametric conditions for the local stability of positive equilibrium point. Moreover, it is shown that there exists Nimark-sacker bifurcation for the unique positive steady-state of given system. In order to control the bifurcation, we introduced a new control strategy. Moreover, some interesting numerical simulations are provided in order to verify the theoretical discussion and to explore the effectiveness and feasibility of new design control strategy.

Keywords prey-predator model;Holling type-II response;nonstandard difference scheme;Nimark-sacker bifurcation;comparison of control techniques.


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