Periodically forced Pielou’s equation

We investigate the global character of solutions of the periodically forced Pielou’s equation xn+1 = βnxn 1+xn−1 , n= 0, 1, . . . , and prove that when the sequence {βn} is periodic with prime period k, with positive values, and k−1 i=0 βi > 1, every positive solution converges to a periodic solution with prime period k. © 2007 Published by Elsevier Inc.