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

Phong, Mai Nam; Khuong, Vu Van

doi:10.22075/ijnaa.2017.1301.1320

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

Document Type : Research Paper

Authors

Mai Nam Phong

Vu Van Khuong

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

10.22075/ijnaa.2017.1301.1320

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

Difference equations

boundedness

persistence

asymptotic behavior

rate of convergence