Analyzing Period-Doubling Bifurcation and Stability for a Discrete-Time Prey- Predator Model with Allee Effect

Abstract

In this study, the qualitative behavior of a discrete time prey-predator model with Allee effect in prey population is discussed. By applying the Euler scheme method to the continuous model in [9], the discretetime model is obtained. First, the existence of the fixed points and their topological classiffications are analyzed algebraically. Then, the conditions of existence for period-doubling bifurcation arising from coexistence fixed point with the help of center manifold theorem are investigated. Finally, numerical simulations are given to support theorical finding.