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

Volume 7, Issue 2 - Serial Number 2
December 2016
Pages 319-329
  • Receive Date: 31 March 2016
  • Revise Date: 19 October 2016
  • Accept Date: 24 November 2016
  • First Publish Date: 20 December 2016