1887
Volume 2014, Issue 1
  • E-ISSN: 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
2019-09-16
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. [1]. Grove   EA., , Ladas   G. . Periodicities in Nonlinear Difference Equations . Boca Raton: : Chapman and Hall/CRC;   2005; .
    [Google Scholar]
  2. [2]. Dehghan   M., , Rastegar   N. . Stability and periodic character of a third order difference equation. . Math Comput Model . 2011; ;54: 11-12 : 2560– 2564 .
    [Google Scholar]
  3. [3]. Dehghan   M., , Mazrooei-Sebdani   R. . Dynamics of a higher-order rational difference equation. . Appl Math Comput . 2006; ;178: 2 : 345– 354 .
    [Google Scholar]
  4. [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 : 756– 775 .
    [Google Scholar]
  5. [5]. Douraki   MJ., , Dehghan   M., , Razavi   A. . On the global behavior of higher order recursive sequences. . Appl Math Comput . 2005; ;169: 2 : 819– 831 .
    [Google Scholar]
  6. [6]. Dehghan   M., , Mazrooei-Sebdani   R. . The characteristics of a higher-order rational difference equation. . Appl Math Comput . 2006; ;182: 1 : 521– 528 .
    [Google Scholar]
  7. [7]. Sedaghat   H. . Nonlinear Difference Equations. Theory with Applications to Social Science Models . Doradrcht: : Kluwer Academic Publishers;   2003; .
    [Google Scholar]
  8. [8]. Dehghan   M., , Douraki   MJ., , Razzaghi   M. . Global behavior of the difference equation . . Chaos Soliton Fract . 2008; ;35: 3 : 543– 549 .
    [Google Scholar]
  9. [9]. Dehghan   M., , Nasri   M., , Razvan   MR. . Global stability of a deterministic model for HIV infection in vivo. . Chaos Soliton Fract . 2007; ;34: 4 : 1225– 1238 .
    [Google Scholar]
  10. [10]. Sedaghat   H. . Geometric stability conditions for higher order difference equations. . J Math Anal Appl . 1998; ;224: 2 : 255– 272 .
    [Google Scholar]
  11. [11]. Dehghan   M., , Mazrooei-Sebdani   R. . Dynamics of . . Appl Math Comput . 2007; ;185: 1 : 464– 472 .
    [Google Scholar]
  12. [12]. Dehghan   M., , Rastegar   N. . On the global behavior of a high-order rational difference equation. . Comput Phys Commun . 2009; ;180: 6 : 873– 878 .
    [Google Scholar]
  13. [13]. Ladas   G. . Open problems and conjectures. . J Differ Equ Appl . 2004; ;10: 9 : 447– 451 .
    [Google Scholar]
  14. [14]. Elsayed   E. . Solutions of rational difference systems of order two. . Math Comput Model . 2012; ;55: 3-4 : 378– 384 .
    [Google Scholar]
  15. [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. [16]. Zheng   Y. . Existence of nonperiodic solutions of the Lyness equation . . J Math Anal Appl . 1997; ;209: 1 : 94– 102 .
    [Google Scholar]
http://instance.metastore.ingenta.com/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