Global and local stability analysis in a nonlinear discrete-time population model

摘要

In this article, we investigate the local and global stability conditions of equilibrium points of discrete-time dynamic model with and without Allee effect. We conclude that the Allee effect decreases both the local stability and the global stability of equilibrium points of the population dynamic model. The results are confirmed with a numerical simulation. MSC: 39A10, 39A30.