Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 241303, 11 pages
http://dx.doi.org/10.1155/2012/241303
Research Article

On the Dynamics of the Recursive Sequence

Mehmet Gümüş,1 Özkan Öcalan,2 and Nilüfer B. Felah2

1Department of Mathematics, Faculty of Science and Arts, Bülent Ecevit University, 67100 Zonguldak, Turkey
2Department of Mathematics, Faculty of Science and Arts, ANS Campus, Afyon Kocatepe University, 03200 Afyonkarahisar, Turkey

Received 5 July 2012; Accepted 13 September 2012

Academic Editor: M. De la Sen

Copyright © 2012 Mehmet Gümüş 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 boundedness character, the oscillatory, and the periodic character of positive solutions of the difference equation , where , , and the initial conditions are arbitrary positive numbers. We investigate the boundedness character for . Also, we investigate the existence of a prime two periodic solution for is odd. Moreover, when is even, we prove that there are no prime two periodic solutions of the equation above.