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Discrete Dynamics in Nature and Society

Volume 2013 (2013), Article ID 963757, 5 pages

http://dx.doi.org/10.1155/2013/963757

Research Article

## Global Behavior of

College of Computer Science, Chongqing University, Chongqing 400044, China

Received 29 June 2013; Revised 9 October 2013; Accepted 16 October 2013

Academic Editor: M. De la Sen

Copyright © 2013 Chenquan Gan 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.

#### Linked References

- M. T. Aboutaleb, M. A. El-Sayed, and A. E. Hamza, “Stability of the recursive sequence ${x}_{n+1}=(\mathrm{\alpha}-{\mathrm{\beta}x}_{n})/(\mathrm{\gamma}+{x}_{n-1})$,”
*Journal of Mathematical Analysis and Applications*, vol. 261, no. 1, pp. 126–133, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - X. Yang, Y. Yang, and J. Luo, “On the difference equation ${x}_{n}=(p+{x}_{n-s})/(q{x}_{n-1}+{x}_{n-s})$,”
*Applied Mathematics and Computation*, vol. 189, no. 1, pp. 918–926, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - R. DeVault, W. Kosmala, G. Ladas, and S. W. Schultz, “Global behavior of ${y}_{n+1}=(p+{y}_{n-k})/(q{y}_{n}+{y}_{n-k})$,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 47, no. 7, pp. 4743–4751, 2001. View at Publisher · View at Google Scholar · View at Scopus - C. H. Gibbons, M. R. S. Kulenović, and G. Ladas, “On the recursive sequence ${x}_{n+1}=(\alpha +{\beta x}_{n-1})/(\gamma +{x}_{n})$,”
*Mathematical Sciences Research Hot-Line*, vol. 4, no. 2, pp. 1–11, 2000. View at Zentralblatt MATH · View at MathSciNet - F. Sun, X. Yang, and C. Zhang, “On the recursive sequence ${x}_{n}=A+{x}_{n-k}^{p}/{x}_{n-1}^{r}$,”
*Discrete Dynamics in Nature and Society*, vol. 2009, Article ID 608976, 8 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - X.-M. Jia and L.-X. Hu, “Global attractivity of a higher-order nonlinear difference equation,”
*International Journal of Difference Equations*, vol. 5, no. 1, pp. 95–101, 2010. View at Zentralblatt MATH · View at MathSciNet - M. Saleh and M. Aloqeili, “On the difference equation ${y}_{n+1}=A+{y}_{n}/{y}_{n-k}$ with $A<0$,”
*Applied Mathematics and Computation*, vol. 176, no. 1, pp. 359–363, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - S. Stević, “On the recursive sequence ${x}_{n+1}={x}_{n-1}/{g(x}_{n})$,”
*Taiwanese Journal of Mathematics*, vol. 6, no. 3, pp. 405–414, 2002. View at Scopus - M. R. S. Kulenović and G. Ladas,
*Dynamics of Second Order Rational Difference Equations with Open Problems and Conjecture*, Chapman and Hall/CRC, Boca Raton, Fla, USA, 1st edition, 2001. View at MathSciNet - S. Stević, “On the recursive sequence ${x}_{n+1}=(\alpha +\beta {x}_{n-1})/{(1+g(x}_{n}))$,”
*Indian Journal of Pure and Applied Mathematics*, vol. 33, no. 12, pp. 1767–1774, 2002. View at Zentralblatt MATH · View at MathSciNet · View at Scopus - M. J. Douraki, M. Dehghan, and M. Razzaghi, “The qualitative behavior of solutions of a nonlinear difference equation,”
*Applied Mathematics and Computation*, vol. 170, no. 1, pp. 485–502, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - S. Stević, “On the recursive sequence ${x}_{n+1}=(\alpha +\beta {x}_{n-k})/{(f(x}_{n},\dots ,{x}_{n-k+1}))$,”
*Taiwanese Journal of Mathematics*, vol. 9, no. 4, pp. 583–593, 2005. View at Zentralblatt MATH · View at MathSciNet · View at Scopus - K. C. Cunningham, M. R. S. Kulenović, G. Ladas, and S. V. Valicenti, “On the recursive sequence ${x}_{n+1}=(\alpha +{\beta x}_{n})/(B{x}_{n}+{Cx}_{n-1})$,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 47, no. 7, pp. 4603–4614, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - L.-X. Hu, W.-T. Li, and S. Stević, “Global asymptotic stability of a second order rational difference equation,”
*Journal of Difference Equations and Applications*, vol. 14, no. 8, pp. 779–797, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - V. L. Kocić and G. Ladas,
*Global Behavior of Nonlinear Difference Equations of Higher Order with Applications*, vol. 256 of*Mathematics and its Applications*, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993. View at MathSciNet - M. R. S. Kulenović and O. Merino, “Global attractivity of the equilibrium of ${x}_{n+1}=(p{x}_{n}+{x}_{n-1})/(q{x}_{n}+{x}_{n-1})$ for $q<p$,”
*Journal of Difference Equations and Applications*, vol. 12, no. 1, pp. 101–108, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - W.-T. Li and H.-R. Sun, “Global attractivity in a rational recursive sequence,”
*Dynamic Systems and Applications*, vol. 11, no. 3, pp. 339–345, 2002. View at Zentralblatt MATH · View at MathSciNet - W. Li, Y. Zhang, and Y. Su, “Global attractivity in a class of higher-order nonlinear difference equation,”
*Acta Mathematica Scientia: Series B*, vol. 25, no. 1, pp. 59–66, 2005. View at Zentralblatt MATH · View at MathSciNet - W. Liu and X. Yang, “Quantitative bounds for positive solutions of a Stević difference equation,”
*Discrete Dynamics in Nature and Society*, vol. 2010, Article ID 235808, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - W. Liu, X. Yang, and J. Cao, “On global attractivity of a class of nonautonomous difference equations,”
*Discrete Dynamics in Nature and Society*, vol. 2010, Article ID 364083, 13 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - S. Stević, “On the difference equation ${x}_{n+1}=\alpha +{x}_{n-1}/{x}_{n}$,”
*Computers & Mathematics with Applications*, vol. 56, no. 5, pp. 1159–1171, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - S. Stević, “Global stability of a max-type difference equation,”
*Applied Mathematics and Computation*, vol. 216, no. 1, pp. 354–356, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - S. Stević, “On a generalized max-type difference equation from automatic control theory,”
*Nonlinear Analysis: Theory, Methods & Applications*, vol. 72, no. 3-4, pp. 1841–1849, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - Y.-H. Su, W.-T. Li, and S. Stević, “Dynamics of a higher order nonlinear rational difference equation,”
*Journal of Difference Equations and Applications*, vol. 11, no. 2, pp. 133–150, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - Y.-H. Su and W.-T. Li, “Global attractivity of a higher order nonlinear difference equation,”
*Journal of Difference Equations and Applications*, vol. 11, no. 10, pp. 947–958, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - X.-X. Yan, W.-T. Li, and H.-R. Sun, “Global attractivity in a higher order nonlinear difference equation,”
*Applied Mathematics E-Notes*, vol. 2, pp. 51–58, 2002. View at Zentralblatt MATH · View at MathSciNet · View at Scopus - X.-X. Yan and W.-T. Li, “Global attractivity in the recursive sequence ${x}_{n+1}=(\alpha -\beta {x}_{n})/(\gamma -{x}_{n-1})$,”
*Applied Mathematics and Computation*, vol. 138, no. 2-3, pp. 415–423, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - X. Yang, W. Liu, and J. Liu, “Global attractivity of a family of max-type difference equations,”
*Discrete Dynamics in Nature and Society*, vol. 2011, Article ID 506373, 12 pages, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - X. Yang, Y. Y. Tang, and J. Cao, “Global asymptotic stability of a family of difference equations,”
*Computers & Mathematics with Applications*, vol. 56, no. 10, pp. 2643–2649, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus - Y. Yang and X. Yang, “On the difference equation ${x}_{n}=(p{x}_{n-s}+{x}_{n-t})/(q{x}_{n-s}+{x}_{n-t})$,”
*Applied Mathematics and Computation*, vol. 203, no. 2, pp. 903–907, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus