Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Cilt: 6 Sayı: 2, 1 - 12
https://doi.org/10.54286/ikjm.1433383

Öz

Kaynakça

  • N. Akgunes, A. S. Kurbanli, On the system of rational difference equations xn = f ¡ xn−a1 , yn−b1 ¢ , yn = g ¡ yn−b2 , zn−c1 ¢ , zn = g ¡ zn−c2 ,xn−a2 ¢ , Selcuk Journal of AppliedMathematics, 15(1), (2014) 1–8.
  • Y. Halim, A. Khelifa, M. Berkal, A. Bounchair, On a solvable system of p difference equations of higher order, PeriodicaMathematica Hungarica, 85(1), (2022) 109–127.
  • A. Ghezal, Note on a rational systemof 4k +4−order difference equations: periodic solution and convergence, Journal of AppliedMathematics & Computing, 69(2), (2023) 2207–2215.
  • A. Ghezal, M. Balegh, I. Zemmouri, Solutions and local stability of the jacobsthal system of difference equations, AIMSMathematics, 9(2), (2024) 3576–3591.
  • M. Gümüş, R. Abo-Zeid, O. Ocalan, Dynamical behavior of a third-order difference equation with arbitrary powers, KyungpookMathematical Journal, 57(2), (2017) 251–263.
  • M. Gümüş, R. Abo-Zeid, Qualitative study of a third order rational systemof difference equations,MathematicaMoravica, 25(1), (2021) 81–97.
  • M. Gümüş, Global asymptotic behavior of a discrete system of difference equations with delays, Filomat, 37(1), (2023) 251–264.
  • M. Gümüş, S. I. Eğilmez, The qualitative analysis of some difference equations using homogeneous functions, Fundamental Journal ofMathematics and Applications, 6(4), 218–231.
  • M. Kara, Y. Yazlik, Solvable three-dimensional system of higher-order nonlinear difference equations, Filomat, 36(10), (2022) 3449–3469
  • M. Kara, Y. Yazlik, On a solvable system of rational difference equations of higher order, Turkish Journal of Mathematics, 46(2), (2022) 587–611.
  • M. Kara, Y. Yazlik, On the solutions of three-dimensional system of difference equations via recursive relations of order two and applications, Journal of Applied Analysis & Computation, 12(2), (2022) 736– 753.
  • M. Kara, Investigation of the global dynamics of two exponential-form difference equations systems, Electronic Research Archive, 31(11), (2023) 6697–6724.
  • A. Khelifa, Y. Halim, General solutions to systems of difference equations and some of their representations, Journal of Applied Mathematics and Computing, 67, (2021) 439–453.
  • N. Taskara, D. T. Tollu, Y. Yazlik, Solutions of rational difference system of order three in terms of padovan numbers, Journal of Advanced Research in Applied Mathematics, 7(3), (2015) 18–29.
  • N. Taskara, D. T. Tollu, N. Touafek, Y. Yazlik, A solvable system of difference equations, Communications of the Korean Mathematical Society, 35(1), (2020) 301–319.
  • D. T. Tollu, I. Yalcinkaya, On solvability of a three-dimensional system of nonlinear difference equations, Dynamics of Continuous, Discrete & Impulsive Systems Series B: Applications & Algorithms, 29(1), (2022) 35–47.
  • I. Yalcinkaya, C. Cinar, D. Simsek, Global asymptotic stability of a system of difference equations, Applicable Analysis, 87, (2008) 677–687.
  • I. Yalcinkaya, D. T. Tollu, Global behavior of a second order system of difference equations, Advanced Studies in ContemporaryMathematics, 26(4), (2016) 653–667.
  • I. Yalcinkaya, H. Ahmad, D. T. Tollu, Y.M. Li, On a system of k-difference equations of order three,Mathematical Problems in Engineering, (2020) 1–11.
  • Y. Yazlik, D. T. Tollu, N. Taskara, On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science, 43(1), (2016) 95–111.
  • T. Koshy, Fibonacci and lucas numbers with applications,Wiley, New York, 2001.
  • S. Stevic, Representation of solutions of bilinear difference equations in terms of generalized fibonacci sequences, Electronic Journal of Qualitative Theory of Differential Equation, 2014(67), (2014) 1–15.
  • D. T. Tollu, Y. Yazlik, N. Taskara, On a solvable nonlinear difference equation of higher order, Turkish Journal ofMathematics, 42, (2018) 1765–1778.
  • M. B. Almatrafi, Exact solution and stability of sixth order difference equations, Electronic Journal of Mathematical Analysis and Applications, 10(1), (2022) 209–225.
  • R. P. Agarwal, E. M. Elsayed, On the solution of fourth-order rational recursive sequence, Advanced Studies in ContemporaryMathematics, 20(4), (2010) 525–545.
  • H. S. Alayachi, M. S. M. Noorani, A. Q. Khan, M. B. Almatrafi, Analytic solutions and stability of sixth order difference equations,Mathematical Problems in Engineering, Article ID 1230979, (2020) 1–12.
  • M. M. El-Dessoky, E. M. Elabbasy, A. Asiri, Dynamics and solutions of a fifth-order nonlinear difference equation, Discrete Dynamics in Nature and Society, Article ID 9129354, (2018) 1–21.
  • M. B. Almatrafi,M.M. Alzubaidi, Qualitative analysis for two fractional difference equations, Nonlinear Engineering, 9(1), (2020) 265–272.
  • E. M. Elabbasy, F. Alzahrani, I. Abbas, N. H. Alotaibi, Dynamical behaviour and solution of nonlinear difference equation via fibonacci sequence, Journal of Applied Analysis and Computation, 10(1), (2020) 282–296.
  • E. M. Elabbasy, F. A. Al-Rakhami, On dynamics and solutions expressions of higher-order rational difference equations, Ikonion Journal ofMathematics, 5(1), (2023) 39–61.
  • E. M. Elabbasy, Qualitative behavior of difference equation of order two, Mathematical and Computer Modellings, 50(2009), (2009) 1130–1141.
  • H. S. Alayachi, M. S. M. Noorani, E. M. Elsayed, Qualitative analysis of a fourth order difference equation, Journal of Applied Analysis and Computation, 10(4), (2020) 1343–1354.
  • T. D. Alharbi, E. M. Elsayed, Forms of solution and qualitative behavior of twelfth-order rational difference equation, International Journal of Difference Equations, 17(2), (2022) 281–292.
  • E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, On the difference equation xn+1 = axn − bxn/(cxn − dxn−1), Advances in Difference Equations, Article ID 82579, (2006) 1–10.
  • N. Touafek, E. M. Elsayed, On a second order rational systems of difference equations, HokkaidoMathematical Journal, 44(1), (2015) 29–45.
  • M. Kara, Y. Yazlik, D. T. Tollu, Solvability of a system of higher order nonlinear difference equations, Hacettepe Journal ofMathematics and Statistics, 49(5), (2020) 1566–1593.
  • S. Elaydi, An introduction to difference equations, Springer, New York, 1996.

Solvability of two-dimensional system of difference equations with constant coefficients

Yıl 2024, Cilt: 6 Sayı: 2, 1 - 12
https://doi.org/10.54286/ikjm.1433383

Öz

In the present paper, the solutions of the following system of difference equations
\begin{equation*}
u_{n}=\alpha_{1}v_{n-2}+\frac{\delta_{1}v_{n-2}u_{n-4}}{\beta_{1}u_{n-4}+\gamma_{1}v_{n-6}}, \ v_{n}=\alpha_{2}u_{n-2}+\frac{\delta_{2}u_{n-2}v_{n-4}}{\beta_{2}v_{n-4}+\gamma_{2}u_{n-6}}, \ n\in \mathbb{N}_{0},
\end{equation*}
where the initial values $u_{-l}$, $v_{-l}$, for $l=\overline{1,6}$ and the parameters $\alpha_{p}$, $\beta_{p}$, $\gamma_{p}$, $\delta_{p}$, for $p\in\{1,2\}$ are non-zero real numbers, are investigated. In addition, the solutions of aforementioned system of difference equations are presented by utilizing Fibonacci sequence when the parameters are equal $1$. Finally, the periodic solutions according to some special cases of the parameters are obtained.

Kaynakça

  • N. Akgunes, A. S. Kurbanli, On the system of rational difference equations xn = f ¡ xn−a1 , yn−b1 ¢ , yn = g ¡ yn−b2 , zn−c1 ¢ , zn = g ¡ zn−c2 ,xn−a2 ¢ , Selcuk Journal of AppliedMathematics, 15(1), (2014) 1–8.
  • Y. Halim, A. Khelifa, M. Berkal, A. Bounchair, On a solvable system of p difference equations of higher order, PeriodicaMathematica Hungarica, 85(1), (2022) 109–127.
  • A. Ghezal, Note on a rational systemof 4k +4−order difference equations: periodic solution and convergence, Journal of AppliedMathematics & Computing, 69(2), (2023) 2207–2215.
  • A. Ghezal, M. Balegh, I. Zemmouri, Solutions and local stability of the jacobsthal system of difference equations, AIMSMathematics, 9(2), (2024) 3576–3591.
  • M. Gümüş, R. Abo-Zeid, O. Ocalan, Dynamical behavior of a third-order difference equation with arbitrary powers, KyungpookMathematical Journal, 57(2), (2017) 251–263.
  • M. Gümüş, R. Abo-Zeid, Qualitative study of a third order rational systemof difference equations,MathematicaMoravica, 25(1), (2021) 81–97.
  • M. Gümüş, Global asymptotic behavior of a discrete system of difference equations with delays, Filomat, 37(1), (2023) 251–264.
  • M. Gümüş, S. I. Eğilmez, The qualitative analysis of some difference equations using homogeneous functions, Fundamental Journal ofMathematics and Applications, 6(4), 218–231.
  • M. Kara, Y. Yazlik, Solvable three-dimensional system of higher-order nonlinear difference equations, Filomat, 36(10), (2022) 3449–3469
  • M. Kara, Y. Yazlik, On a solvable system of rational difference equations of higher order, Turkish Journal of Mathematics, 46(2), (2022) 587–611.
  • M. Kara, Y. Yazlik, On the solutions of three-dimensional system of difference equations via recursive relations of order two and applications, Journal of Applied Analysis & Computation, 12(2), (2022) 736– 753.
  • M. Kara, Investigation of the global dynamics of two exponential-form difference equations systems, Electronic Research Archive, 31(11), (2023) 6697–6724.
  • A. Khelifa, Y. Halim, General solutions to systems of difference equations and some of their representations, Journal of Applied Mathematics and Computing, 67, (2021) 439–453.
  • N. Taskara, D. T. Tollu, Y. Yazlik, Solutions of rational difference system of order three in terms of padovan numbers, Journal of Advanced Research in Applied Mathematics, 7(3), (2015) 18–29.
  • N. Taskara, D. T. Tollu, N. Touafek, Y. Yazlik, A solvable system of difference equations, Communications of the Korean Mathematical Society, 35(1), (2020) 301–319.
  • D. T. Tollu, I. Yalcinkaya, On solvability of a three-dimensional system of nonlinear difference equations, Dynamics of Continuous, Discrete & Impulsive Systems Series B: Applications & Algorithms, 29(1), (2022) 35–47.
  • I. Yalcinkaya, C. Cinar, D. Simsek, Global asymptotic stability of a system of difference equations, Applicable Analysis, 87, (2008) 677–687.
  • I. Yalcinkaya, D. T. Tollu, Global behavior of a second order system of difference equations, Advanced Studies in ContemporaryMathematics, 26(4), (2016) 653–667.
  • I. Yalcinkaya, H. Ahmad, D. T. Tollu, Y.M. Li, On a system of k-difference equations of order three,Mathematical Problems in Engineering, (2020) 1–11.
  • Y. Yazlik, D. T. Tollu, N. Taskara, On the solutions of a three-dimensional system of difference equations, Kuwait Journal of Science, 43(1), (2016) 95–111.
  • T. Koshy, Fibonacci and lucas numbers with applications,Wiley, New York, 2001.
  • S. Stevic, Representation of solutions of bilinear difference equations in terms of generalized fibonacci sequences, Electronic Journal of Qualitative Theory of Differential Equation, 2014(67), (2014) 1–15.
  • D. T. Tollu, Y. Yazlik, N. Taskara, On a solvable nonlinear difference equation of higher order, Turkish Journal ofMathematics, 42, (2018) 1765–1778.
  • M. B. Almatrafi, Exact solution and stability of sixth order difference equations, Electronic Journal of Mathematical Analysis and Applications, 10(1), (2022) 209–225.
  • R. P. Agarwal, E. M. Elsayed, On the solution of fourth-order rational recursive sequence, Advanced Studies in ContemporaryMathematics, 20(4), (2010) 525–545.
  • H. S. Alayachi, M. S. M. Noorani, A. Q. Khan, M. B. Almatrafi, Analytic solutions and stability of sixth order difference equations,Mathematical Problems in Engineering, Article ID 1230979, (2020) 1–12.
  • M. M. El-Dessoky, E. M. Elabbasy, A. Asiri, Dynamics and solutions of a fifth-order nonlinear difference equation, Discrete Dynamics in Nature and Society, Article ID 9129354, (2018) 1–21.
  • M. B. Almatrafi,M.M. Alzubaidi, Qualitative analysis for two fractional difference equations, Nonlinear Engineering, 9(1), (2020) 265–272.
  • E. M. Elabbasy, F. Alzahrani, I. Abbas, N. H. Alotaibi, Dynamical behaviour and solution of nonlinear difference equation via fibonacci sequence, Journal of Applied Analysis and Computation, 10(1), (2020) 282–296.
  • E. M. Elabbasy, F. A. Al-Rakhami, On dynamics and solutions expressions of higher-order rational difference equations, Ikonion Journal ofMathematics, 5(1), (2023) 39–61.
  • E. M. Elabbasy, Qualitative behavior of difference equation of order two, Mathematical and Computer Modellings, 50(2009), (2009) 1130–1141.
  • H. S. Alayachi, M. S. M. Noorani, E. M. Elsayed, Qualitative analysis of a fourth order difference equation, Journal of Applied Analysis and Computation, 10(4), (2020) 1343–1354.
  • T. D. Alharbi, E. M. Elsayed, Forms of solution and qualitative behavior of twelfth-order rational difference equation, International Journal of Difference Equations, 17(2), (2022) 281–292.
  • E. M. Elabbasy, H. El-Metwally, E. M. Elsayed, On the difference equation xn+1 = axn − bxn/(cxn − dxn−1), Advances in Difference Equations, Article ID 82579, (2006) 1–10.
  • N. Touafek, E. M. Elsayed, On a second order rational systems of difference equations, HokkaidoMathematical Journal, 44(1), (2015) 29–45.
  • M. Kara, Y. Yazlik, D. T. Tollu, Solvability of a system of higher order nonlinear difference equations, Hacettepe Journal ofMathematics and Statistics, 49(5), (2020) 1566–1593.
  • S. Elaydi, An introduction to difference equations, Springer, New York, 1996.
Toplam 37 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Adi Diferansiyel Denklemler, Fark Denklemleri ve Dinamik Sistemler
Bölüm Makaleler
Yazarlar

Ömer Aktaş 0000-0002-5763-0308

Merve Kara 0000-0001-8081-0254

Yasin Yazlik 0000-0001-6369-540X

Erken Görünüm Tarihi 25 Temmuz 2024
Yayımlanma Tarihi
Gönderilme Tarihi 7 Şubat 2024
Kabul Tarihi 4 Nisan 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 6 Sayı: 2

Kaynak Göster

APA Aktaş, Ö., Kara, M., & Yazlik, Y. (2024). Solvability of two-dimensional system of difference equations with constant coefficients. Ikonion Journal of Mathematics, 6(2), 1-12. https://doi.org/10.54286/ikjm.1433383
AMA Aktaş Ö, Kara M, Yazlik Y. Solvability of two-dimensional system of difference equations with constant coefficients. ikjm. Temmuz 2024;6(2):1-12. doi:10.54286/ikjm.1433383
Chicago Aktaş, Ömer, Merve Kara, ve Yasin Yazlik. “Solvability of Two-Dimensional System of Difference Equations With Constant Coefficients”. Ikonion Journal of Mathematics 6, sy. 2 (Temmuz 2024): 1-12. https://doi.org/10.54286/ikjm.1433383.
EndNote Aktaş Ö, Kara M, Yazlik Y (01 Temmuz 2024) Solvability of two-dimensional system of difference equations with constant coefficients. Ikonion Journal of Mathematics 6 2 1–12.
IEEE Ö. Aktaş, M. Kara, ve Y. Yazlik, “Solvability of two-dimensional system of difference equations with constant coefficients”, ikjm, c. 6, sy. 2, ss. 1–12, 2024, doi: 10.54286/ikjm.1433383.
ISNAD Aktaş, Ömer vd. “Solvability of Two-Dimensional System of Difference Equations With Constant Coefficients”. Ikonion Journal of Mathematics 6/2 (Temmuz 2024), 1-12. https://doi.org/10.54286/ikjm.1433383.
JAMA Aktaş Ö, Kara M, Yazlik Y. Solvability of two-dimensional system of difference equations with constant coefficients. ikjm. 2024;6:1–12.
MLA Aktaş, Ömer vd. “Solvability of Two-Dimensional System of Difference Equations With Constant Coefficients”. Ikonion Journal of Mathematics, c. 6, sy. 2, 2024, ss. 1-12, doi:10.54286/ikjm.1433383.
Vancouver Aktaş Ö, Kara M, Yazlik Y. Solvability of two-dimensional system of difference equations with constant coefficients. ikjm. 2024;6(2):1-12.