Period-doubling Bifurcation and Stability in a Two Dimensional Discrete Prey-predator Model with Allee Effect and Immigration Parameter on Prey

This article is about the dynamics of a discrete-time prey-predator system with Allee effect and immigration parameter on prey population. Particularly, we study existence local asymptotic stability unique positive fixed point. Furthermore, conditions for bifurcation in are derived. In addition, it shown that goes through period-doubling by using theory center manifold theorem. Eventually, numerical examples given to illustrate theoretical results.