1887
Volume 2014, Issue 1
  • EISSN: 2223-506X

Abstract

In this paper, we investigate the nature of the solutions to the following difference equation:

where the initial values , α, β, B, C are positive and k ∈ {1,2,3,…} is fixed.

We study the boundedness nature and global behavior of its solutions. Also, we investigate the analysis of the semi-cycles under special conditions.

Loading

Article metrics loading...

/content/journals/10.5339/connect.2014.10
2014-07-01
2024-10-05
Loading full text...

Full text loading...

/deliver/fulltext/connect/2014/1/connect.2014.10.html?itemId=/content/journals/10.5339/connect.2014.10&mimeType=html&fmt=ahah

References

  1. Grove EA, Ladas G. Periodicities in Nonlinear Difference Equations. Boca Raton: Chapman and Hall/CRC 2005.
    [Google Scholar]
  2. Dehghan M, Rastegar N. Stability and periodic character of a third order difference equation. Math Comput Model. 2011; 54:11-12:25602564.
    [Google Scholar]
  3. Dehghan M, Mazrooei-Sebdani R. Dynamics of a higher-order rational difference equation. Appl Math Comput. 2006; 178:2:345354.
    [Google Scholar]
  4. Dehghan M, Douraki MJ, Douraki MJ. Dynamics of a rational difference equation using both theoretical and computational approaches. Appl Math Comput. 2005; 168:2:756775.
    [Google Scholar]
  5. Douraki MJ, Dehghan M, Razavi A. On the global behavior of higher order recursive sequences. Appl Math Comput. 2005; 169:2:819831.
    [Google Scholar]
  6. Dehghan M, Mazrooei-Sebdani R. The characteristics of a higher-order rational difference equation. Appl Math Comput. 2006; 182:1:521528.
    [Google Scholar]
  7. Sedaghat H. Nonlinear Difference Equations. Theory with Applications to Social Science Models. Doradrcht: Kluwer Academic Publishers 2003.
    [Google Scholar]
  8. Dehghan M, Douraki MJ, Razzaghi M. Global behavior of the difference equation . Chaos Soliton Fract. 2008; 35:3:543549.
    [Google Scholar]
  9. Dehghan M, Nasri M, Razvan MR. Global stability of a deterministic model for HIV infection in vivo. Chaos Soliton Fract. 2007; 34:4:12251238.
    [Google Scholar]
  10. Sedaghat H. Geometric stability conditions for higher order difference equations. J Math Anal Appl. 1998; 224:2:255272.
    [Google Scholar]
  11. Dehghan M, Mazrooei-Sebdani R. Dynamics of . Appl Math Comput. 2007; 185:1:464472.
    [Google Scholar]
  12. Dehghan M, Rastegar N. On the global behavior of a high-order rational difference equation. Comput Phys Commun. 2009; 180:6:873878.
    [Google Scholar]
  13. Ladas G. Open problems and conjectures. J Differ Equ Appl. 2004; 10:9:447451.
    [Google Scholar]
  14. Elsayed E. Solutions of rational difference systems of order two. Math Comput Model. 2012; 55:3-4:378384.
    [Google Scholar]
  15. Kulenovic MRS, Ladas G. Dynamics of second order rational. Differential equations with open problems and conjectures. Boca Raton: Chapman and Hall/CRC 2002.
    [Google Scholar]
  16. Zheng Y. Existence of nonperiodic solutions of the Lyness equation . J Math Anal Appl. 1997; 209:1:94102.
    [Google Scholar]
/content/journals/10.5339/connect.2014.10
Loading
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error