Muhammad Salman Khan Muhammad Asif Khan Muhammad Sajjad Shabbir Qamar Din Department of Mathematics, Quaid-I-Azam University Islamabad, 44230, Pakistan Department of Mathematics, University of the PoonchRawalakot, Rawalakot 12350, Pakistan Department of Mathematics, Air University Islamabad, 44230, Pakistan Network Biology ISSN 2220-8879 http://www.iaees.org/publications/journals/nb/online-version.asp 2019 9 3 58 77 International Academy of Ecology and Environmental Sciences Hong Kong 11 May 2019 10 June 2019 1 September 2019 prey-predator model Holling type-II response nonstandard difference scheme Nimark-sacker bifurcation comparison of control techniques 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. http://www.iaees.org/publications/journals/nb/articles/2019-9(3)/stability-bifurcation-and-chaos-control-in-a-prey-predator-model.pdf