Discrete Dynamics in Nature and SocietyVolume 2006, Article ID 90625, 12 pageshttp://dx.doi.org/10.1155/DDNS/2006/90625

## On the global behavior of the nonlinear difference equation xn+1=f(pn,xn−m,xn−t(k+1)+1)

1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China

Received 7 February 2006; Accepted 5 April 2006

Copyright © 2006 Taixiang Sun and Hongjian Xi. 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.

1. A. M. Amleh, E. A. Grove, G. Ladas, and D. A. Georgiou, “On the recursive sequence $x_{n + 1} = \alpha + {{x_{n - 1} } \mathord{\left/ {\vphantom {{x_{n - 1} } {x_n }}} \right. \kern-\nulldelimiterspace} {x_n }}$,” Journal of Mathematical Analysis and Applications, vol. 233, no. 2, pp. 790–798, 1999.
2. R. DeVault, C. Kent, and W. and Kosmala, “On the recursive sequence $x_{n + 1} = p + {{x_{n - k} } \mathord{\left/ {\vphantom {{x_{n - k} } {x_n }}} \right. \kern-\nulldelimiterspace} {x_n }}$,” Journal of Difference Equations and Applications, vol. 9, no. 8, pp. 721–730, 2003.
3. C. H. Gibbons, M. R. S. Kulenović, and G. Ladas, “On the recursive sequence ${{x_{n + 1} = (\alpha + \beta x_{n - 1} )} \mathord{\left/ {\vphantom {{x_{n + 1} = (\alpha + \beta x_{n - 1} )} {(\gamma + x_n )}}} \right. \kern-\nulldelimiterspace} {(\gamma + x_n )}}$,” Mathematical Sciences Research Hot-Line, vol. 4, no. 2, pp. 1–11, 2000.
4. M. R. S. Kulenović, G. Ladas, and C. B. Overdeep, “On the dynamics of $x_{n + 1} = p_n + {{x_{n - 1} } \mathord{\left/ {\vphantom {{x_{n - 1} } {x_n }}} \right. \kern-\nulldelimiterspace} {x_n }}$ with a period-two coefficient,” Journal of Difference Equations and Applications, vol. 10, no. 10, pp. 905–914, 2004.
5. G. Ladas, “Progress report on ${{x_{n + 1} = (\alpha + \beta x_n + \gamma x_{n - 1} )} \mathord{\left/ {\vphantom {{x_{n + 1} = (\alpha + \beta x_n + \gamma x_{n - 1} )} {(A + Bx_n + Cx_{n - 1} )}}} \right. \kern-\nulldelimiterspace} {(A + Bx_n + Cx_{n - 1} )}}$,” Journal of Difference Equations and Applications, vol. 5, no. 3, pp. 211–215, 1995.
6. G. Papaschinopoulos and C. J. Schinas, “On a $(k + 1)$-th order difference equation with a coefficient of period $k + 1$,” Journal of Difference Equations and Applications, vol. 11, no. 3, pp. 215–225, 2005.