Global Asymptotic Stability of a Nonautonomous Difference Equation

Abstract

We study the following nonautonomous difference equation: $x_{n+1}={(x}_n{x}_{n-1}+p_n)/(x_n+x_{n-1})$, $n=\mathrm{0,1},\dots$, where $p_n>0$ is a period-2 sequence and the initial values $x_{-1},x_0\in (0,\infty )$. We show that the unique prime period-2 solution of the equation above is globally asymptotically stable.