Asymptotic behavior of a system of two difference equations of exponential form

Document Type: Research Paper

Authors

Department of Mathematical Analysis, University of Transport and Communications, Hanoi City, Vietnam

Abstract

In this paper, we study the boundedness and persistence of the solutions, the global stability of the unique positive equilibrium point and the rate of convergence of a solution that converges to the equilibrium $E=(\bar{x},\ \bar{y})$ of the system of two difference equations of exponential form:
\begin{equation*}
x_{n+1}=\dfrac{a+e^{-(bx_n+cy_n)}}{d+bx_n+cy_n},\ y_{n+1}=\dfrac{a+e^{-(by_n+cx_n)}}{d+by_n+cx_n}
\end{equation*}
where $a,\ b,\ c,\ d$ are positive constants and the initial values $ x_0,\ y_0$ are positive real values.

Keywords