Global asymptotic stability for two recursive difference equations

摘要

Two sufficient conditions are obtained for the global asymptotic stability of the following two recursive difference equationsxn+1=xnxn−1+xn−2+axn+xn−1xn−2+a,n=0,1,2,…,andxn+1=xn−1+xnxn−2+axnxn−1+xn−2+a,n=0,1,2,…,where a∈[0,∞) and the initial values x−2,x−1,x0∈(0,∞). Some known results are included.