Global Asymptotic Stability of a Nonautonomous Difference Equation

Abstract

We study the following nonautonomous difference equation: xn+1=(xnxn-1+pn)/(xn+xn-1), n=0,1,…, where pn>0 is a period-2 sequence and the initial values x-1,x0∈(0,∞). We show that the unique prime period-2 solution of the equation above is globally asymptotically stable.