Copyright © 2009 D. M. Chan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the global behavior of the second-order difference equation xn+1=xn−1((αxn+βxn−1)/(Axn+Bxn−1)), where initial conditions and all coefficients are positive. We find conditions on A,B,α,β under which the even and odd subsequences of a positive solution converge, one to zero and the other to a nonnegative number; as well as conditions where one of the subsequences diverges to infinity and the other either converges to a positive number or diverges to infinity. We also find initial conditions where the solution monotonically converges to zero and where it diverges to infinity.