Global behavior of a discrete population model

Abstract

<abstract><p>In this work, the global behavior of a discrete population model</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \begin{cases} x_{n+1}& = \alpha x_n e^{-y_n}+\beta,\\ y_{n+1}& = \alpha x_n(1-e^{-y_n}), \end{cases}\quad n = 0,1,2,\dots, \end{equation*} $\end{document} </tex-math></disp-formula></p> <p>is considered, where $ \alpha\in (0, 1) $, $ \beta\in (0, +\infty) $, and the initial value $ (x_{0}, y_0)\in [0, \infty)\times [0, \infty) $. To illustrate the dynamics behavior of this model, the boundedness, periodic character, local stability, bifurcation, and the global asymptotic stability of the solutions are investigated.</p></abstract>