Global asymptotic stability for two recursive difference equations

Abstract

Two sufficient conditions are obtained for the global asymptotic stability of the following two recursive difference equations x n+1= x nx n−1+x n−2+a x n+x n−1x n−2+a , n=0,1,2,…, and x n+1= x n−1+x nx n−2+a x nx n−1+x n−2+a , n=0,1,2,…, where a∈[0,∞) and the initial values x −2, x −1, x 0∈(0,∞). Some known results are included.