Özlem Ak Gümüş

Stability analysis of a general discrete-time population model involving delay and Allee effects

Abstract In this paper, we investigate stability conditions of equilibrium points of a general delay difference population model with and without Allee effects which occur at low population density. The analysis demonstrates that Allee effects have both stabilizing and destabilizing effects on population dynamics including time delay.

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

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.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.

Global Stability Analysis of a General Scalar Difference Equation

We consider a general first order scalar difference equation with and without Allee effect. The model without Allee effect represents asexual reproduction of a species while the model including Allee effect represents sexual reproduction. We analyze global stabilities of both models analytically and compare the results obtained. Numerical simulations are included to support the analytical results. We conclude that Allee effect decreases global stability of a nonnegative fixed point of the model. This result is different from the local stability behavior of the same fixed point of the model.

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

The author would like to apologize for some errors which are published in Ref. [1].