Abstract and Applied Analysis
Volume 2009 (2009), Article ID 152964, 10 pages
doi:10.1155/2009/152964

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

Taixiang Sun1 , Bin Qin2 , Hongjian Xi2 and Caihong Han1

1College of Mathematics and Information Science, Guangxi University, Nanning 530004, China
 2Department of Mathematics, Guangxi College of Finance and Economics, Nanning 530003, China

Abstract

We study global behavior of the following max-type difference equation xn+1=max⁡{1/xn,An/xn−1}, n=0,1,…, where {An}n=0∞ is a sequence of positive real numbers with 0≤inf⁡An≤sup⁡An<1. The special case when {An}n=0∞ is a periodic sequence with period k and An∈(0,1) for every n≥0 has been completely investigated by Y. Chen. Here we extend his results to the general case.