Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2021, Cilt: 9 Sayı: 1, 1 - 9, 28.04.2021

Erkan Taşdemir , Yüksel Soykan

Öz

Kaynakça

  • [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 Nonlinear Analysis and Applications, 2(2) (2011), 24-43.
  • [17] C.M. Kent, W. Kosmala and S. Stevic}, Long-term behavior of solutions of the difference equation $x_{n+1}=x_{n-1}x_{n-2}-1$, Abstr. Appl. Anal., 2010 (2010), 1-17.
  • [18] C.M. Kent, W. Kosmala and S. Stevic, On the difference equation $x_{n+1}=x_{n}x_{n-2}-1$, Abstr. Appl. Anal., 2011 (2011), 1-15.
  • [19] E. Taşdemir, On the Asymptotically Periodic Solutions of A Fifth Order Difference Equation, J. Math. Anal., 10(3) (2019), 100-111.
  • [20] E. Ta\c{s}demir, On The Dynamics of a Nonlinear Difference Equation, Adıyaman University Journal of Science, 9(1) (2019), 190-201.
  • [21] E. Taşdemir and Y. Soykan, On the Periodicies of the Difference Equation $x_{n+1}=x_{n}x_{n-1}+\alpha $, Karaelmas Science and Engineering Journal, 6(2) (2016), 329-333.
  • [22] E. Taşdemir and Y. Soykan, Long-Term Behavior of Solutions of the Non-Linear Difference Equation $ x_{n+1}=x_{n-1}x_{n-3}-1$, Gen. Math. Notes, 38(1) (2017), 13-31.
  • [23] E. Taşdemir and Y. Soykan, Stability of Negative Equilibrium of a Non-Linear Difference Equation, J. Math. Sci. Adv. Appl., 49(1) (2018), 51-57.
  • [24] E. Taşdemir and Y. Soykan, Dynamical Analysis of a Non-Linear Difference Equation, J. Comput. Anal. Appl., 26(2) (2019), 288-301.
  • [25] Y. Wang, Y. Luo and Z. Lu, Convergence of solutions of $x_{n+1}=x_{n}x_{n-1}-1$, Appl. Math. E-Notes, 12 (2012), 153-157.
  • [26] A.S. Kurbanli , C. Çınar and İ. Yalçinkaya, On the behavior of positive solutions of the system of rational difference equations $x_{n+1}=x_{n-1}/y_{n}x_{n-1}+1$, $ y_{n+1}=y_{n-1}/x_{n}y_{n-1}+1$, Mathematical and Computer Modelling, 53(5-6) (2011), 1261-1267.
  • [27] A.S. Kurbanli, On the Behavior of Solutions of the System of Rational Difference Equations: $ x_{n+1}=x_{n-1}/y_{n}x_{n-1}+1,y_{n+1}=y_{n-1}/x_{n}y_{n-1}+1,z_{n+1}=z_{n-1}/y_{n}z_{n-1}+1 $, Discrete Dyn. Nat. Soc., 2011 (2011), 1-12.
  • [28] V.L. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Vol. 256, Springer Science & Business Media, 1993.
  • [29] M. Kara and Y. Yazlık, Solvability of a system of nonlinear difference equations of higher order, Turkish J. Math., 43 (2019), 1533-1565.

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

Yıl 2021, Cilt: 9 Sayı: 1, 1 - 9, 28.04.2021

Erkan Taşdemir , Yüksel Soykan

Öz

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.

Anahtar Kelimeler

boundedness difference equations dynamical systems periodicity stability

Kaynakça

  • [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 Nonlinear Analysis and Applications, 2(2) (2011), 24-43.
  • [17] C.M. Kent, W. Kosmala and S. Stevic}, Long-term behavior of solutions of the difference equation $x_{n+1}=x_{n-1}x_{n-2}-1$, Abstr. Appl. Anal., 2010 (2010), 1-17.
  • [18] C.M. Kent, W. Kosmala and S. Stevic, On the difference equation $x_{n+1}=x_{n}x_{n-2}-1$, Abstr. Appl. Anal., 2011 (2011), 1-15.
  • [19] E. Taşdemir, On the Asymptotically Periodic Solutions of A Fifth Order Difference Equation, J. Math. Anal., 10(3) (2019), 100-111.
  • [20] E. Ta\c{s}demir, On The Dynamics of a Nonlinear Difference Equation, Adıyaman University Journal of Science, 9(1) (2019), 190-201.
  • [21] E. Taşdemir and Y. Soykan, On the Periodicies of the Difference Equation $x_{n+1}=x_{n}x_{n-1}+\alpha $, Karaelmas Science and Engineering Journal, 6(2) (2016), 329-333.
  • [22] E. Taşdemir and Y. Soykan, Long-Term Behavior of Solutions of the Non-Linear Difference Equation $ x_{n+1}=x_{n-1}x_{n-3}-1$, Gen. Math. Notes, 38(1) (2017), 13-31.
  • [23] E. Taşdemir and Y. Soykan, Stability of Negative Equilibrium of a Non-Linear Difference Equation, J. Math. Sci. Adv. Appl., 49(1) (2018), 51-57.
  • [24] E. Taşdemir and Y. Soykan, Dynamical Analysis of a Non-Linear Difference Equation, J. Comput. Anal. Appl., 26(2) (2019), 288-301.
  • [25] Y. Wang, Y. Luo and Z. Lu, Convergence of solutions of $x_{n+1}=x_{n}x_{n-1}-1$, Appl. Math. E-Notes, 12 (2012), 153-157.
  • [26] A.S. Kurbanli , C. Çınar and İ. Yalçinkaya, On the behavior of positive solutions of the system of rational difference equations $x_{n+1}=x_{n-1}/y_{n}x_{n-1}+1$, $ y_{n+1}=y_{n-1}/x_{n}y_{n-1}+1$, Mathematical and Computer Modelling, 53(5-6) (2011), 1261-1267.
  • [27] A.S. Kurbanli, On the Behavior of Solutions of the System of Rational Difference Equations: $ x_{n+1}=x_{n-1}/y_{n}x_{n-1}+1,y_{n+1}=y_{n-1}/x_{n}y_{n-1}+1,z_{n+1}=z_{n-1}/y_{n}z_{n-1}+1 $, Discrete Dyn. Nat. Soc., 2011 (2011), 1-12.
  • [28] V.L. Kocic and G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, Vol. 256, Springer Science & Business Media, 1993.
  • [29] M. Kara and Y. Yazlık, Solvability of a system of nonlinear difference equations of higher order, Turkish J. Math., 43 (2019), 1533-1565.
Toplam 29 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Erkan Taşdemir 0000-0002-5002-3193

Yüksel Soykan

Yayımlanma Tarihi 28 Nisan 2021
Gönderilme Tarihi 2 Temmuz 2019
Kabul Tarihi 27 Ekim 2020
Yayımlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

APA Taşdemir, 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, 9(1), 1-9.
AMA Taşdemir E, Soykan Y. 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 J. Math. Nisan 2021;9(1):1-9.
Chicago Taşdemir, Erkan, ve Yüksel Soykan. “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 9, sy. 1 (Nisan 2021): 1-9.
EndNote Taşdemir E, Soykan Y (01 Nisan 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 9 1 1–9.
IEEE E. Taşdemir ve Y. Soykan, “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 J. Math., c. 9, sy. 1, ss. 1–9, 2021.
ISNAD Taşdemir, Erkan - Soykan, Yüksel. “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 9/1 (Nisan 2021), 1-9.
JAMA Taşdemir E, Soykan Y. 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 J. Math. 2021;9:1–9.
MLA Taşdemir, Erkan ve Yüksel Soykan. “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, c. 9, sy. 1, 2021, ss. 1-9.
Vancouver Taşdemir E, Soykan Y. 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 J. Math. 2021;9(1):1-9.
 Kapak Resmi İndir
Creative Commons License
The published articles in KJM are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.