Global Stability of Beddington Model

Abstract

We discuss qualitative behavior of a discrete-time density-dependent predator-prey model. More precisely, we discuss the existence and uniqueness of positive steady-state, permanence, local and global behavior of unique positive equilibrium point and the rate of convergence of positive solutions that converge to the unique positive equilibrium point of this model. Moreover, it is also proved that system undergoes Neimark–Sacker bifurcation by using standard mathematical techniques of bifurcation theory. Numerical simulations are provided to illustrate theoretical discussion.