Global Behavior of the Max-Type Difference Equation xn+1=max⁡{1/xn,An/xn−1}

Abstract

We study global behavior of the following max-type difference equation $x_{n+1}=\max \left\{1/x_n,A_n/x_{n-1}\right\}$, $n=0,1,\dots ,$ where ${\left\{A_n\right\}}_{n=0}^{\infty }$ is a sequence of positive real numbers with $0\le \inf A_n\le \sup A_n<1$. The special case when ${\left\{A_n\right\}}_{n=0}^{\infty }$ is a periodic sequence with period $k$ and $A_n\in \left(0,1\right)$ for every $n\ge 0$ has been completely investigated by Y. Chen. Here we extend his results to the general case.