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

Document Type : Research Paper


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


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:
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}
where $a,\ b,\ c,\ d$ are positive constants and the initial values $ x_0,\ y_0$ are positive real values.


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