Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 791610, 10 pages
doi:10.1155/2010/791610
Research Article

Asymptotic Stability for a Class of Nonlinear Difference Equations

Chang-you Wang,1,2,3 Shu Wang,3 Zhi-wei Wang,4 Fei Gong,2,5 and Rui-fang Wang2,5

1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network Control & Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China
3College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
4School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
5College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 9 January 2010; Accepted 5 February 2010

Academic Editor: Guang Zhang

Copyright © 2010 Chang-you Wang 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

  1. W. Li and H. Sun, “Global attractivity in a rational recursive sequence,” Dynamic Systems and Applications, vol. 11, pp. 339–346, 2002. View at Zentralblatt MATH
  2. A. M. Amleh, N. Kruse, and G. Ladas, “On a class of difference equations with strong negative feedback,” Journal of Difference Equations and Applications, vol. 5, no. 6, pp. 497–515, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. K. Cunningham, M. R. S. Kulenovic, G. Ladas, and S. V. Valicenti, “On the recursive sequence xn+1=(α+βxn)/(Bxn+Cxn−1),” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, pp. 4603–4614, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. L. Li, “Stability properties of nonlinear difference equations and conditions for boundedness,” Computers & Mathematics with Applications, vol. 38, pp. 29–35, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. M. R. S. Kulenovic, G. Ladas, and N. R. Prokup, “A rational difference equation,” Computers & Mathematics with Applications, vol. 41, pp. 671–678, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X. Yan, W. Li, and H. Sun, “Global attractivity in a higher order nonlinear difference equation,” Applied Mathematics E-Notes, vol. 2, pp. 51–58, 2002. View at Zentralblatt MATH
  7. G. Ladas, “Open problem and conjectures,” Journal of Difference Equations and Applications, vol. 3, pp. 317–321, 1997.
  8. T. Nesemann, “Positive nonlinear difference equations: some results and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 47, no. 7, pp. 4707–4717, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. X. Li and D. Zhu, “Global asymptotic stability of a nonlinear recursive sequence,” Applied Mathematics Letters, vol. 17, no. 7, pp. 833–838, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. Yang, W. Su, B. Chen, G. M. Megson, and D. J. Evans, “On the recursive sequence xn+1=(axn−1+bxn−2)/(c+dxn−1xn−2),” Applied Mathematics and Computation, vol. 162, pp. 1485–1497, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. K. S. Berenhaut, J. D. Foley, and S. Stevic, “The global attractivity of the rational difference equation yn=(yn−k+yn−m)/(1+yn−kyn−m),” Applied Mathematics Letters, vol. 20, pp. 54–58, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. K. S. Berenhaut and S. Stevic, “The difference equation xn+1=(a+xn−k)/∑i=0k−1cixn−i has solutions converging to zero,” Journal of Mathematical Analysis and Applications, vol. 326, pp. 1466–1471, 2007.
  13. C. Wang, “Existence and stability of periodic solutions for parabolic systems with time delays,” Journal of Mathematical Analysis and Applications, vol. 339, no. 2, pp. 1354–1361, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C. Wang and S. Wang, “Oscillation of partial population model with diffusion and delay,” Applied Mathematics Letters, vol. 22, no. 12, pp. 1793–1797, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. C. Wang, S. Wang, and X. Yan, “Global asymptotic stability of 3-species mutualism models with diffusion and delay effects,” Discrete Dynamics in Natural and Science, vol. 2009, Article ID 317298, 20 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. C. F. Li and Y. Zhou, “Existence of bounded and unbounded non-oscillatory solutions for partial difference equations,” Mathematical and Computer Modelling, vol. 45, pp. 825–833, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. Wang, F. Gong, S. Wang, L. Li, and Q. Shi, “Asymptotic behavior of equilibrium point for a class of nonlinear difference equation,” Advances in Difference Equations, vol. 2009, Article ID 214309, 8 pages, 2009. View at Publisher · View at Google Scholar
  18. S. M. Chen and C. S. Li, “Nonoscillatory solutions of second order nonlinear difference equations,” Applied Mathematics and Computation, vol. 205, no. 1, pp. 478–481, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. T. Sun and H. Xi, “Global attractivity for a family of nonlinear difference equations,” Applied Mathematics Letters, vol. 20, no. 7, pp. 741–745, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Z. Q. Liu, Y. G. Xu, and S. M. Kang, “Global solvability for a second order nonlinear neutral delay difference equation,” Computers and Mathematics with Applications, vol. 57, no. 4, pp. 587–595, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. M. R. S. Kulenovic and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC Press, Boca Raton, Fla, USA, 2001.
  22. V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.