Periodically forced Pielou's equation

We investigate the global character of solutions of the periodically forced Pielou's equation xn+1 = beta(n)x(n)/1+x(n-1), n = 0,1,..., and prove that when the sequence {beta(n)} is periodic with prime period k, with positive values, and Pi(k-1)(i=0)beta(i) > 1, every positive solution converges to a periodic solution with prime period k. (c) 2007 Published by Elsevier Inc.