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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 241303, 11 pages
doi:10.1155/2012/241303
On the Dynamics of the Recursive Sequence
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.