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Dergiler / Ikonion Journal of Mathematics / 2026 / Volume: 2 Issue: 1

A solvable system of nonlinear difference equations

Abdullah Şahinkaya(NECMETTİN ERBAKAN ÜNİVERSİTESİ)
İbrahim Yalçınkaya(NECMETTİN ERBAKAN ÜNİVERSİTESİ, FEN FAKÜLTESİ)
Durhasan Turgut Tollu(NECMETTİN ERBAKAN ÜNİVERSİTESİ, FEN FAKÜLTESİ)
Sayfa
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Yayın Tarihi
2020-07-30
DOI
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Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀ where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form.
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Temel Bulgular & Veri:In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀ where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form.
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Sonuç & Katkı:Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Asymptotic behavior · explicit solution · nonlinear difference equation

Abstract

In this paper, we show that the following systems of nonlinear difference equations x_{n+1}=((x_{n}y_{n}+a)/(x_{n}+y_{n})),y_{n+1}=((y_{n}z_{n}+a)/(y_{n}+z_{n})),z_{n+1}=((z_{n}x_{n}+a)/(z_{n}+x_{n})) for n∈ℕ₀ where a∈[0,∞) and the initial values x₀, y₀, z₀ are real numbers, can be solved in explicit form. Also, we investigate the asymptotic behavior of the solutions by using these formulae and give some numerical examples which verify our theoretical result.

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Bu Makaleye Atıf Yap

Şahinkaya, A., Yalçınkaya, İ., Tollu, D. T. (2020). A solvable system of nonlinear difference equations. Ikonion Journal of Mathematics, Volume: 2 Issue: 1. https://ajindex.com/articles/1492821

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Kaynakça (24)

  1. R. Abu-Saris, C. Cinar and I. Yalcinkaya, On the asymptotic stability of x_{n+1}=((x_{n}x_{n-k}+a)/(x_{n}+x_{n-k})), Computers & Mathematics with Applications, 56(5) (2008), 1172--1175.
  2. N. Akgunes, A. S. Kurbanli, On the system of rational difference equations x_{n}=f(x_{n-a₁},y_{n-b₁}), y_{n}=g(y_{n-b₂},z_{n-c₁}), z_{n}=g(z_{n-c₂},x_{n-a₂}), Selcuk Journal of Applied Mathematics, 15(1) (2014), 8 pages.
  3. Dekkar, N. Touafek and Y. Yazlik, Global stability of a third-order nonlinear system of difference equations with period-two coefficients, Revista de la real academia de ciencias exactas, f ísicas y naturales. Serie A. Matemáticas, 111 (2017), 325-347.
  4. M. Gümüş and Y. Soykan, Global character of a six-dimensional nonlinear system of difference equations, Discrete Dynamics in Nature and Society, Article ID 6842521 (2016), 7 pages.
  5. N. Haddad, N. Touafek and J. F. T. Rabago, Solution form of a higher-order system of difference equations and dynamical behavior of its special case, Mathematical Methods in the Applied Sciences, 40 (2017), 3599-3607.
  6. N. Haddad, N. Touafek and J. F. T. Rabago, Well-defined solutions of a system of difference equations, Journal of Applied Mathematics and Computing, 56 (2018), 439-458.
  7. M. Kara and Y. Yazlik, Solvability of a system of nonlinear difference equations of higher order, Turkish Journal of Mathematics, 43 (3)(2019), 1533-1565.
  8. A. S. Kurbanli, C. Çinar and D. Şimşek, On the periodicity of solutions of the system of rational difference equations, Applied Mathematics, 2 (2011), 410-413.
  9. A. S. Kurbanli, C. Çinar and D. Şimşek, 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.
  10. O. Ozkan and A. S. Kurbanli, On a system of difference equations, Discrete Dynamics in Nature and Society, Article ID 970316, (2013), 7 pages.
  11. S. Stević, M. A. Alghamdi, A. Alotaibi and E. M. Elsayed, Solvable product-type system of difference equations of second order, Electronic Journal of Differential Equations, 2015, No:169, (2015), 1-20.
  12. S. Stević, New class of solvable systems of difference equations, Applied Mathematics Letters, 63(2017), 137-144.
  13. D. T. Tollu, Y. Yazlik and N. Taskara, On fourteen solvable systems of difference equations, Applied Mathematics and Computation, 233 (2014), 310-319.
  14. I. Yalcinkaya, C. Cinar and D. Simsek, Global asymptotic stability of a system of difference equations, Applicable Analysis, 87(6)(2008), 677-687, DOI: 10.1080/00036810802140657.
  15. I. Yalcinkaya, On the global asymptotic stability of a second-order system of difference equations, Discrete Dynamics in Nature and Society, vol. 2008, Article ID 860152, 12 pages, 2008. doi:10.1155/2008/860152.
  16. I. Yalcinkaya and D. T. Tollu, Global behavior of a second-order system of difference equations, Advanced Studies in Contemporary Mathematics, 26(4)(2016), 653-667.
  17. X. Li and D. Zhu, Global asymptotic stability in a rational equation, Journal of Difference Equations and Applications, 9(9)(2003), 833-839.
  18. Y. Yazlik, E. M. Elsayed and N. Taskara, On the behaviour of the solutions of difference equation systems, Journal of Computational Analysis & Applications, 16(5)(2014), 932-941.
  19. Y. Yazlik, D. T. Tollu and N. Taskara, On the behaviour of solutions for some systems of difference equations, Journal of Computational Analysis & Applications, 18(1)(2015), 166-178.
  20. Y. Yazlik, D. T. Tollu and N. Taskara, On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences, 38(17)(2015), 4388-4410.
  21. Y. Yazlik, D. T. Tollu and N. Taskara, On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science 43(1)(2016), 95-111.
  22. Y. Yazlik and M. Kara, On a solvable system of difference equations of higher-order with period two coefficients, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2) (2019), 1675-1693.
  23. I. Yalcinkaya, C. Cinar and D. Simsek, Global asymptotic stability of a system of difference equations, Applicable Analysis, 87(6)(2008), 677-687, DOI: 10.1080/00036810802140657.
  24. X. Li and D. Zhu, Global asymptotic stability in a rational equation, Journal of Difference Equations and Applications, 9(9)(2003), 833-839.