On the Global Asymptotic Stability of a Second‐Order System of Difference Equations

Abstract

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations z n +1 = ( t n z n −1 + a )/( t n + z n −1 ), t n +1 = ( z n t n −1 + a )/( z n + t n −1 ), n = 0, 1, 2, …, where the parameter a ϵ (0, ∞ ) and the initial values ( z k , t k ) ϵ (0, ∞ ) (for k = −1, 0).