title: Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model.
abstract: In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey model in the closed first quadrant [Formula: see text]. The existence and local stability of the unique positive equilibrium of the model are analyzed algebraically. It is shown that the model can undergo a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium and an invariant circle will appear. Some numerical simulations are presented to illustrate our theocratical results and numerically it is shown that the unique positive equilibrium of the system is globally asymptotically stable.
authors.affiliation: Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad, 13100 Pakistan ; Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240 China.
authors.forename: A Q
authors.initials: AQ
authors.lastname: Khan
keywords: Bifurcation theory; Neimark-Sacker bifurcation; Predator-prey model; Stability