SavedAdd your journal

Journals / Konuralp Journal of Mathematics / 2021 / Cilt: 9 - Sayı: 1

On the Dynamics of a System of Difference Equations $x_{n+1}=x_{n-1}y_{n}-1, y_{n+1}=y_{n-1}z_{n}-1, z_{n+1}=z_{n-1}x_{n}-1$

Erkan TAŞDEMİR
Yüksel SOYKAN
Pages
1–9
Publication Date
2021-04-28
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Especially we investigate the periodicity, boundedness and stability of related system of difference equations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study the dynamics of following system of nonlinear difference equations $x_{n+1}=x_{n-1}y_{n}-1,$ $y_{n+1}=y_{n-1}z_{n}-1,$ $ z_{n+1}=z_{n-1}x_{n}-1$.
📊
Key Findings & Data:In this paper, we study the dynamics of following system of nonlinear difference equations $x_{n+1}=x_{n-1}y_{n}-1,$ $y_{n+1}=y_{n-1}z_{n}-1,$ $ z_{n+1}=z_{n-1}x_{n}-1$.
💡
Conclusion & Impact:Especially we investigate the periodicity, boundedness and stability of related system of difference equations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:boundedness · difference equations · dynamical systems

Abstract

In this paper, we study the dynamics of following system of nonlinear difference equations $x_{n+1}=x_{n-1}y_{n}-1,$ $y_{n+1}=y_{n-1}z_{n}-1,$ $ z_{n+1}=z_{n-1}x_{n}-1$. Especially we investigate the periodicity, boundedness and stability of related system of difference equations.

🔖

Cite This Article

TAŞDEMİR, E., SOYKAN, Y. (2021). On the Dynamics of a System of Difference Equations $x_{n+1}=x_{n-1}y_{n}-1, y_{n+1}=y_{n-1}z_{n}-1, z_{n+1}=z_{n-1}x_{n}-1$. Konuralp Journal of Mathematics, Cilt: 9 - Sayı: 1, 1–9. https://ajindex.com/articles/786391

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. K. Liu, P. Li, F. Han and W. Zhong, Behavior of the Difference Equations $x_{n+1}=x_{n}x_{n-1}-1$, J. Comput. Anal. Appl., 22(7) (2017), 1361-1370
  2. İ. Okumuş and Y. Soykan, On the Stability of a Nonlinear Difference Equation, Asian Journal of Mathematics and Computer Research, 17(2) (2017), 88-110
  3. İ. Okumuş and Y. Soykan, Some Technique To Show The Boundedness Of Rational Difference Equations, Journal of Progressive Research in Mathematics, 13(2) (2018), 2246-2258
  4. İ. Okumuş and Y. Soykan, Dynamical behavior of a system of three-dimensional nonlinear difference equations, Adv. Difference Equ., 2018:224 (2018), 1-15
  5. G. Papaschinopoulos and C.J. Schinas, On a system of two nonlinear difference equations, J. Math. Anal. Appl., 219(2) (1998), 415-426
  6. S. Stevic, M.A. Alghamdi, D.A. Maturi and N. Shahzad, On the Periodicity of Some Classes of Systems of Nonlinear Difference Equations. Abstr. Appl. Anal., 2014 (2014), 1-6
  7. R.P. Agarwal and P.J. Wong, Advanced topics in difference equations (Vol. 404), Springer Science \& Business Media, 2013
  8. E. Camouzis and G. Ladas, Dynamics of third order rational difference equations with open problems and conjectures, volume 5 of Advances in Discrete Mathematics and Applications, Chapman \& Hall/CRC, Boca Raton, 2008
  9. E. Camouzis and G. Papaschinopoulos, Global asymptotic behavior of positive solutions on the system of rational difference equations $x_{n+1}=1+x_{n}/y_{n-m}$, $y_{n+1}=1+y_{n}/x_{n-m}$, Appl. Math. Lett., 17(6) (2004), 733-737
  10. Q. Din, M.N. Qureshi and A.Q. Khan, Dynamics of a fourth-order system of rational difference equations, Adv. Difference Equ., 2012:215 (2012), 1-15
  11. S. Elaydi, An Introduction to Difference Equations, Springer-Verlag, 1996
  12. A. Gelisken and M. Kara, Some general systems of rational difference equations, Journal of Difference Equations, 2015 (2015), 1-7
  13. M. Göcen and M. Güneysu, The global attractivity of some rational difference equations, J. Comput. Anal. Appl., 25(7) (2018), 1233-1243
  14. M. Göcen and A. Cebeci, On the Periodic Solutions of Some Systems of Higher Order Difference Equations, Rocky Mountain J. Math., 48(3) (2018), 845-858
  15. C.M. Kent, W. Kosmala, M.A. Radin and S. Stevic, Solutions of the difference equation $x_{n+1}=x_{n}x_{n-1}-1$, Abstr. Appl. Anal., 2010 (2010), 1-13
  16. C.M. Kent, W. Kosmala, On the Nature of Solutions of the Difference Equation $x_{n+1}=x_{n}x_{n-3}-1$, International Journal of Nonl