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Solution of a Solvable System of Difference Equation

Year 2022, Volume: 4 Issue: 1, 1 - 8, 23.09.2022

Ali Gelişken Murat Arı

https://doi.org/10.54286/ikjm.1050493

Abstract

In this study we give solutions for the following difference equation sytem
x_{n+1}= (a.x_{n}y_{n-3}/y_{n-2}-\alpha)+\beta y_{n+1}=(b.x_{n-3}y_{n}/x_{n-2}-\beta) +\alpha n ∈N0
where the parameters a,b,, and initial values x_{-i}, y_{-i}, i=0,1,2,3 are non-zero real numbers. We show the asymptotic behavior of the system of equation.

Keywords

Difference equations Periodicity System of difference equations Asymptotic behavior

References

  • Elabbasy, E.M., El-Metwally, H., Elsayed, E.M. (2007) Qualitative behavior of higher order difference equation. Soochow J. Math. 33, 861–873. Elaydi, S. (1999) An Introduction to Difference Equations. Springer, New York.
  • Papaschinopoulos, G., Fotiades, N., Schinas, C.J. (2014) On a system of difference equations including negative exponential terms. J. Differ. Equ. Appl. 20, 717–732.
  • Haddad, N., Touafek, N. and Rabago, JFT. (2018) “Well-defined solutions of a system of difference equations”, Journal of Appl. Math. and Comput., 56(1-2), 439-458.
  • Kara, M. , Touafek, N. , Yazlik, Y. (2020) Well-Defined Solutions of a Three-Dimensional System of Difference Equations. Gazi University Journal of Science 33, 767-778.
  • Stevi´c, S. (2012) On a solvable rational system of difference equations.Appl.Math. Comput. 219, 2896–2908.
  • Stevi´c, S. (2013) On a solvable system of difference equations of kth order. Appl. Math. Comput. 219 , 7765–7771.
  • Stevi´c, S. (2011) On a system of difference equations. Appl. Math. Comput. 218 , 3372–3378.
  • Stevi´c, S. (2011) On a system of difference equations with period two coefficients. Appl.Math. Comput. 218, 4317–4324.
  • Yazlik, Y., Elsayed, E.M., Taskara, N. (2014) On the behaviour of the solutions the solutions of difference equation system. J. Comput. Anal. Appl. 16(5), 932–941.
  • Tollu DT, Yalçınkaya İ, Ahmad H, Yao SW. (2021) A detailed study on a solvable system related to the linear fractional difference equation. Math Biosci Eng. Jun 17;18(5):5392-5408
  • Şahinkaya, A. , Yalçınkaya, İ. & Tollu, D. T. (2020) A solvable system of nonlinear difference equations . Ikonion Journal of Mathematics , 2 (1) , 10-20 .
  • Simsek, D., Ogul,B. and Abdullayev,F. (2020) Solution of the Rational Difference Equation x_{n+1}= x_{n-13} /(1+ x_{n-1} x_{n-3} x_{n-5} x_{n-7} x_{n-9} x_{n-11} ). Applied Mathematics and Nonlinear Sciences,5(1) 485-494.
  • Simsek, D., Ogul,B and Abdullayev,F. (2017) Solutions of the rational difference equations x_{n+1}= x_{n-11} /(1+ x_{n-2} x_{n-5} x_{n-8}) , AIP Conference Proceedings 1880, 040003 Karatas, R., & Gelisken, A. (2011) Qualitative behavior of a rational difference equation. Ars Combinatoria, 100, 321-326.
  • Karatas, R. (2017) Global behavior of a higher order difference equation International Journal of Contemporary Mathematical Sciences, Vol. 12, no. 3, 133-138
  • Kurbanli, A. S. (2011). On the behavior of solutions of the system of rational difference equations. Advances in Difference Equations. 10.1186/1687-1847-2011-40.
  • Kurbanli, A. S., Çinar, C. & Şimşek, D. (2011) On the Periodicity of Solutions of the System of Rational Difference Equations. Applied Mathematics. 02. 410-413. 10.4236/am.2011.24050.

Year 2022, Volume: 4 Issue: 1, 1 - 8, 23.09.2022

Ali Gelişken Murat Arı

https://doi.org/10.54286/ikjm.1050493

Abstract

References

  • Elabbasy, E.M., El-Metwally, H., Elsayed, E.M. (2007) Qualitative behavior of higher order difference equation. Soochow J. Math. 33, 861–873. Elaydi, S. (1999) An Introduction to Difference Equations. Springer, New York.
  • Papaschinopoulos, G., Fotiades, N., Schinas, C.J. (2014) On a system of difference equations including negative exponential terms. J. Differ. Equ. Appl. 20, 717–732.
  • Haddad, N., Touafek, N. and Rabago, JFT. (2018) “Well-defined solutions of a system of difference equations”, Journal of Appl. Math. and Comput., 56(1-2), 439-458.
  • Kara, M. , Touafek, N. , Yazlik, Y. (2020) Well-Defined Solutions of a Three-Dimensional System of Difference Equations. Gazi University Journal of Science 33, 767-778.
  • Stevi´c, S. (2012) On a solvable rational system of difference equations.Appl.Math. Comput. 219, 2896–2908.
  • Stevi´c, S. (2013) On a solvable system of difference equations of kth order. Appl. Math. Comput. 219 , 7765–7771.
  • Stevi´c, S. (2011) On a system of difference equations. Appl. Math. Comput. 218 , 3372–3378.
  • Stevi´c, S. (2011) On a system of difference equations with period two coefficients. Appl.Math. Comput. 218, 4317–4324.
  • Yazlik, Y., Elsayed, E.M., Taskara, N. (2014) On the behaviour of the solutions the solutions of difference equation system. J. Comput. Anal. Appl. 16(5), 932–941.
  • Tollu DT, Yalçınkaya İ, Ahmad H, Yao SW. (2021) A detailed study on a solvable system related to the linear fractional difference equation. Math Biosci Eng. Jun 17;18(5):5392-5408
  • Şahinkaya, A. , Yalçınkaya, İ. & Tollu, D. T. (2020) A solvable system of nonlinear difference equations . Ikonion Journal of Mathematics , 2 (1) , 10-20 .
  • Simsek, D., Ogul,B. and Abdullayev,F. (2020) Solution of the Rational Difference Equation x_{n+1}= x_{n-13} /(1+ x_{n-1} x_{n-3} x_{n-5} x_{n-7} x_{n-9} x_{n-11} ). Applied Mathematics and Nonlinear Sciences,5(1) 485-494.
  • Simsek, D., Ogul,B and Abdullayev,F. (2017) Solutions of the rational difference equations x_{n+1}= x_{n-11} /(1+ x_{n-2} x_{n-5} x_{n-8}) , AIP Conference Proceedings 1880, 040003 Karatas, R., & Gelisken, A. (2011) Qualitative behavior of a rational difference equation. Ars Combinatoria, 100, 321-326.
  • Karatas, R. (2017) Global behavior of a higher order difference equation International Journal of Contemporary Mathematical Sciences, Vol. 12, no. 3, 133-138
  • Kurbanli, A. S. (2011). On the behavior of solutions of the system of rational difference equations. Advances in Difference Equations. 10.1186/1687-1847-2011-40.
  • Kurbanli, A. S., Çinar, C. & Şimşek, D. (2011) On the Periodicity of Solutions of the System of Rational Difference Equations. Applied Mathematics. 02. 410-413. 10.4236/am.2011.24050.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Ali Gelişken

Murat Arı

Early Pub Date March 10, 2022
Publication Date September 23, 2022
Acceptance Date February 21, 2022
Published in Issue Year 2022 Volume: 4 Issue: 1

Cite

APA Gelişken, A., & Arı, M. (2022). Solution of a Solvable System of Difference Equation. Ikonion Journal of Mathematics, 4(1), 1-8. https://doi.org/10.54286/ikjm.1050493
AMA Gelişken A, Arı M. Solution of a Solvable System of Difference Equation. ikjm. September 2022;4(1):1-8. doi:10.54286/ikjm.1050493
Chicago Gelişken, Ali, and Murat Arı. “Solution of a Solvable System of Difference Equation”. Ikonion Journal of Mathematics 4, no. 1 (September 2022): 1-8. https://doi.org/10.54286/ikjm.1050493.
EndNote Gelişken A, Arı M (September 1, 2022) Solution of a Solvable System of Difference Equation. Ikonion Journal of Mathematics 4 1 1–8.
IEEE A. Gelişken and M. Arı, “Solution of a Solvable System of Difference Equation”, ikjm, vol. 4, no. 1, pp. 1–8, 2022, doi: 10.54286/ikjm.1050493.
ISNAD Gelişken, Ali - Arı, Murat. “Solution of a Solvable System of Difference Equation”. Ikonion Journal of Mathematics 4/1 (September 2022), 1-8. https://doi.org/10.54286/ikjm.1050493.
JAMA Gelişken A, Arı M. Solution of a Solvable System of Difference Equation. ikjm. 2022;4:1–8.
MLA Gelişken, Ali and Murat Arı. “Solution of a Solvable System of Difference Equation”. Ikonion Journal of Mathematics, vol. 4, no. 1, 2022, pp. 1-8, doi:10.54286/ikjm.1050493.
Vancouver Gelişken A, Arı M. Solution of a Solvable System of Difference Equation. ikjm. 2022;4(1):1-8.
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