Research Article
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Year 2023, Volume: 6 Issue: 1, 24 - 34, 29.03.2023
https://doi.org/10.33401/fujma.1166022

Abstract

References

  • [1] M. M. El-Dessoky, E. M. Elsayed, M. Alghamdi, Solutions and periodicity for some systems of fourth-order rational difference equations, J. Comp. Ana. Appl., 18 (1)(2015), 179-194.
  • [2] M. M. El-Dessoky, A. Khaliq, A. Asiri, On some rational systems of difference equations, J. Nonlinear Sci.Appl., 11 (1) (2017), 49-72.
  • [3] H. El-Metwally, E. M. Elsayed, Solution and behavior of a third rational difference equation, Utilitas Math., 88 (2012), 27-42.
  • [4] M. El-Moneam, On the dynamics of the solutions of the rational recursive sequences, British J. Math. Comp.Sci., 5 (5) (2015), 654-665.
  • [5] E. M. Elsayed, Solutions of rational difference system of order two, Math. Comp. Mod., 55 (2012), 378-384.
  • [6] E. M. Elsayed, On the solutions of a rational system of difference equations, Fasciculi Math., 45 (2010), 25-36.
  • [7] E. M. Elsayed, Solution and attractivity for a rational recursive sequence, Disc.Dyn. Nat. Soc., 2011, article ID 982309, 17 pages.
  • [8] C. Cinar, I. Yalcınkaya, R. Karatas, On the positive solutions of the difference equation system $x_{n+1}=\frac{m}{y_{n}}, y_{n+1}=\frac{py_{n}}{x_{n-1}y_{n-1}}$, J. Inst. Math. Comp. Sci., 18 (2005), 135-136.
  • [9] M. M. El-Dessoky, E. M. Elsayed, On the solutions and periodic nature of some systems of rational difference equations, J. Comp. Ana. Appl., 18 (2) (2015), 206-218, (2018), 444-453.
  • [10] A. S. Kurbanli, C. Cinar, D. Simsek, On the periodicity of solutions of the system of rational difference equations $x_{n+1}=\frac{x_{n-1}+y_{n}}{x_{n-1} y_{n}-1}, y_{n+1}=\frac{y_{n-1}+x_{n}}{y_{n-1} x_{n}-1}$, Appl. Math., 2 (2011), 410-413.
  • [11] M. M. El-Dessoky, The form of solutions and periodicity for some systems of third-order rational difference equations, Math. Meth. Appl.Sci., 39 (2016), 1076-1092.
  • [12] N. Touafek, E. Elsayed, On a second order rational systems of difference equations, Hokkaido Math. J., 44 (1) (2015), 29-45.
  • [13] I. Yalcnkaya, On the global asymptotic behavior of a system of two nonlinear difference equations, ARS Comb., 95 (2010), 151-159.
  • [14] E. M. Elsayed, J. G. Al-Jauid, H. MAlaikah, On the Solutions of Systems of Rational Difference Equations, J. Prog. Rese.Math., 19(2) (2022), 49-59.
  • [15] X. Yang, Y. Liu, S. Bai, On the system of high order rational difference equations $x_{n}=\frac{a}{y_{n-p}},$ $y_{n}=\frac{by_{n-p}}{x_{n-q}y_{n-q}}$, Appl. Math. Comp., 171(2) (2005), 853-856.
  • [16] N. Touafek, E. M. Elsayed, On the solutions of systems of rational difference equations, Math. Comput. Mod., 55(2012), 1987-1997.
  • [17] Turki D. Alharbi, E. M. Elsayed, Forms of Solution and Qualitative Behavior of Twelfth-Order Rational DifferenceEquation, Int. J. Differ. Equ., 17(2) (2022), 281-292.
  • [18] M. Mansour, M. M. El-Dessoky, E. M. Elsayed, The form of the solutions and periodicity of some systems of difference equations, Disc. Dyn. Nat. Soc., 2012, article ID 406821, 17 pages.
  • [19] E. M. Elsayed, H. S. Gafel, Dynamics and global stability of second order nonlinear difference equation, Pan-American J. Math., 1 (2022), 1-16.
  • [20] E. M. Elsayed, A. Alshareef, Faris Alzahrani, Qualitative behavior and solutionof asystem of three-dimensionsl rational difference equations, Math. Meth. Appl. Sci., 45 (2022), 5456-5470.
  • [21] E. M. Elsayed, B. S. Alofi, A. Q. Khan, Solution Expressions of Discrete Systems of Difference Equations, Math.Problem Engin. , (2022), ID Article 3678257, 14 pages.
  • [22] E. M. Elsayed, M. M. El-Dessoky, Dynamics and behavior of a higher order rational recursive sequence, Adv. Differ. Equ., 2012 (2012), 69.
  • [23] A. Kurbanli, C. Cinar, I. Yalcınkaya, On the behavior of positive solutions of the system of rational difference equations, Math. Comp. Mod., 53 (2011), 1261-1267.
  • [24] I. Yalcınkaya, On the global asymptotic stability of a second-order system of difference equations, Disc. Dyn. Nat. Soc., 2008, article ID 860152, 12 pages.
  • [25] I. Yalcınkaya, C. Cinar, M. Atalay, On the solutions of systems of difference equations, Adv. Differ. Equ., 2008, article ID 143943, 9 pages.

The Form of Solutions and Periodic Nature for Some System of Difference Equations

Year 2023, Volume: 6 Issue: 1, 24 - 34, 29.03.2023
https://doi.org/10.33401/fujma.1166022

Abstract

In this paper, we study the form of the solution of the following systems of difference equations of order two

w_{n+1}=\frac{w_{n}s_{n-1}}{w_{n}+s_{n-1}},~~~ s_{n+1}=\frac{s_{n}w_{n-1}}{\pm s_{n}\pm w_{n-1}},

with nonzero real numbers initial conditions.

References

  • [1] M. M. El-Dessoky, E. M. Elsayed, M. Alghamdi, Solutions and periodicity for some systems of fourth-order rational difference equations, J. Comp. Ana. Appl., 18 (1)(2015), 179-194.
  • [2] M. M. El-Dessoky, A. Khaliq, A. Asiri, On some rational systems of difference equations, J. Nonlinear Sci.Appl., 11 (1) (2017), 49-72.
  • [3] H. El-Metwally, E. M. Elsayed, Solution and behavior of a third rational difference equation, Utilitas Math., 88 (2012), 27-42.
  • [4] M. El-Moneam, On the dynamics of the solutions of the rational recursive sequences, British J. Math. Comp.Sci., 5 (5) (2015), 654-665.
  • [5] E. M. Elsayed, Solutions of rational difference system of order two, Math. Comp. Mod., 55 (2012), 378-384.
  • [6] E. M. Elsayed, On the solutions of a rational system of difference equations, Fasciculi Math., 45 (2010), 25-36.
  • [7] E. M. Elsayed, Solution and attractivity for a rational recursive sequence, Disc.Dyn. Nat. Soc., 2011, article ID 982309, 17 pages.
  • [8] C. Cinar, I. Yalcınkaya, R. Karatas, On the positive solutions of the difference equation system $x_{n+1}=\frac{m}{y_{n}}, y_{n+1}=\frac{py_{n}}{x_{n-1}y_{n-1}}$, J. Inst. Math. Comp. Sci., 18 (2005), 135-136.
  • [9] M. M. El-Dessoky, E. M. Elsayed, On the solutions and periodic nature of some systems of rational difference equations, J. Comp. Ana. Appl., 18 (2) (2015), 206-218, (2018), 444-453.
  • [10] A. S. Kurbanli, C. Cinar, D. Simsek, On the periodicity of solutions of the system of rational difference equations $x_{n+1}=\frac{x_{n-1}+y_{n}}{x_{n-1} y_{n}-1}, y_{n+1}=\frac{y_{n-1}+x_{n}}{y_{n-1} x_{n}-1}$, Appl. Math., 2 (2011), 410-413.
  • [11] M. M. El-Dessoky, The form of solutions and periodicity for some systems of third-order rational difference equations, Math. Meth. Appl.Sci., 39 (2016), 1076-1092.
  • [12] N. Touafek, E. Elsayed, On a second order rational systems of difference equations, Hokkaido Math. J., 44 (1) (2015), 29-45.
  • [13] I. Yalcnkaya, On the global asymptotic behavior of a system of two nonlinear difference equations, ARS Comb., 95 (2010), 151-159.
  • [14] E. M. Elsayed, J. G. Al-Jauid, H. MAlaikah, On the Solutions of Systems of Rational Difference Equations, J. Prog. Rese.Math., 19(2) (2022), 49-59.
  • [15] X. Yang, Y. Liu, S. Bai, On the system of high order rational difference equations $x_{n}=\frac{a}{y_{n-p}},$ $y_{n}=\frac{by_{n-p}}{x_{n-q}y_{n-q}}$, Appl. Math. Comp., 171(2) (2005), 853-856.
  • [16] N. Touafek, E. M. Elsayed, On the solutions of systems of rational difference equations, Math. Comput. Mod., 55(2012), 1987-1997.
  • [17] Turki D. Alharbi, E. M. Elsayed, Forms of Solution and Qualitative Behavior of Twelfth-Order Rational DifferenceEquation, Int. J. Differ. Equ., 17(2) (2022), 281-292.
  • [18] M. Mansour, M. M. El-Dessoky, E. M. Elsayed, The form of the solutions and periodicity of some systems of difference equations, Disc. Dyn. Nat. Soc., 2012, article ID 406821, 17 pages.
  • [19] E. M. Elsayed, H. S. Gafel, Dynamics and global stability of second order nonlinear difference equation, Pan-American J. Math., 1 (2022), 1-16.
  • [20] E. M. Elsayed, A. Alshareef, Faris Alzahrani, Qualitative behavior and solutionof asystem of three-dimensionsl rational difference equations, Math. Meth. Appl. Sci., 45 (2022), 5456-5470.
  • [21] E. M. Elsayed, B. S. Alofi, A. Q. Khan, Solution Expressions of Discrete Systems of Difference Equations, Math.Problem Engin. , (2022), ID Article 3678257, 14 pages.
  • [22] E. M. Elsayed, M. M. El-Dessoky, Dynamics and behavior of a higher order rational recursive sequence, Adv. Differ. Equ., 2012 (2012), 69.
  • [23] A. Kurbanli, C. Cinar, I. Yalcınkaya, On the behavior of positive solutions of the system of rational difference equations, Math. Comp. Mod., 53 (2011), 1261-1267.
  • [24] I. Yalcınkaya, On the global asymptotic stability of a second-order system of difference equations, Disc. Dyn. Nat. Soc., 2008, article ID 860152, 12 pages.
  • [25] I. Yalcınkaya, C. Cinar, M. Atalay, On the solutions of systems of difference equations, Adv. Differ. Equ., 2008, article ID 143943, 9 pages.
There are 25 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Elsayed Elsayed 0000-0003-0894-8472

J. Al-juaid 0000-0001-6062-5916

Publication Date March 29, 2023
Submission Date August 23, 2022
Acceptance Date December 5, 2022
Published in Issue Year 2023 Volume: 6 Issue: 1

Cite

APA Elsayed, E., & Al-juaid, J. (2023). The Form of Solutions and Periodic Nature for Some System of Difference Equations. Fundamental Journal of Mathematics and Applications, 6(1), 24-34. https://doi.org/10.33401/fujma.1166022
AMA Elsayed E, Al-juaid J. The Form of Solutions and Periodic Nature for Some System of Difference Equations. Fundam. J. Math. Appl. March 2023;6(1):24-34. doi:10.33401/fujma.1166022
Chicago Elsayed, Elsayed, and J. Al-juaid. “The Form of Solutions and Periodic Nature for Some System of Difference Equations”. Fundamental Journal of Mathematics and Applications 6, no. 1 (March 2023): 24-34. https://doi.org/10.33401/fujma.1166022.
EndNote Elsayed E, Al-juaid J (March 1, 2023) The Form of Solutions and Periodic Nature for Some System of Difference Equations. Fundamental Journal of Mathematics and Applications 6 1 24–34.
IEEE E. Elsayed and J. Al-juaid, “The Form of Solutions and Periodic Nature for Some System of Difference Equations”, Fundam. J. Math. Appl., vol. 6, no. 1, pp. 24–34, 2023, doi: 10.33401/fujma.1166022.
ISNAD Elsayed, Elsayed - Al-juaid, J. “The Form of Solutions and Periodic Nature for Some System of Difference Equations”. Fundamental Journal of Mathematics and Applications 6/1 (March 2023), 24-34. https://doi.org/10.33401/fujma.1166022.
JAMA Elsayed E, Al-juaid J. The Form of Solutions and Periodic Nature for Some System of Difference Equations. Fundam. J. Math. Appl. 2023;6:24–34.
MLA Elsayed, Elsayed and J. Al-juaid. “The Form of Solutions and Periodic Nature for Some System of Difference Equations”. Fundamental Journal of Mathematics and Applications, vol. 6, no. 1, 2023, pp. 24-34, doi:10.33401/fujma.1166022.
Vancouver Elsayed E, Al-juaid J. The Form of Solutions and Periodic Nature for Some System of Difference Equations. Fundam. J. Math. Appl. 2023;6(1):24-3.

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