The Form of the Solutions of System of Rational Difference Equation
Abstract
In this article, we study the form of the solutions of the system of difference equations $x_{n+1}=((y_{n-8})/(1+y_{n-2}x_{n-5}y_{n-8}))$, $y_{n+1}=((x_{n-8})/(\pm1\pm x_{n-2}y_{n-5}x_{n-8}))$, with the initial conditions are real numbers. Also, we give the numerical examples of some of difference equations and got some related graphs and figures using by Matlab.
Keywords
References
- [1] A. M. Ahmed, E. M. Elsayed, The expressions of solutions and the periodicity of some rational difference equations system, J. Appl. Math. Inform. 34(1-2) (2016), 35–48.
- [2] 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.
- [3] M. M. El-Dessoky, E. M. Elsayed, On the solutions and periodic nature of some systems of rational difference equations, J. Comput. Anal. Appl., 18(2) (2015), 206–218.
- [4] M. M. El-Dessoky, A. Khaliq, A. Asiri, On some rational system of difference equations, J. Nonlinear Sci. Appl., 11 (2018), 49–72.
- [5] E. M. Elsayed, T. F. Ibrahim, Periodicity and solutions for some systems of nonlinear rational difference equations, Hacettepe Journal of Mathematics and Statistics, 44 (6) (2015), 1361–1390.
- [6] E. M. Elsayed, A. Alghamdi, The form of the solutions of nonlinear difference equations systems, J. Nonlinear Sci. Appl., 9 (2016), 3179–3196.
- [7] N. Haddad , N. Touafek, J. F. T. Rabago, Solution form of a higher-order system of difference equations and dynamical behavior of its special case, Math. Methods Appl. Sci., 40 (2017), 3599–3607.
- [8] A. S. Kurbanli, On the behavior of solutions of the system of rational difference equations $x_{n+1}=x_{n-1}/(y_{n}x_{n-1}-1),$; $y_{n+1}=y_{n-1}/(x_{n}y_{n-1}-1)$, World Appl. Sci. J., 10(11) (2010), 1344-1350.
- [9] A. S. Kurbanli, C. C¸ inar, D. S¸ims¸ek, On the periodicity of solutions of the system of rational difference equations $x_{n+1}=x_{n-1}+y_{n}/(y_{n}x_{n-1}-1),$; $y_{n+1}=y_{n-1}+x_{n}/(x_{n}y_{n-1}-1)$, Appl. Math., 2 (2011), 410-413.
- [10] A. S. Kurbanli, C. C¸ inar, I. Yalc¸inkaya, On the behavior of positive solutions of the system of rational difference equations $x_{n+1}=x_{n-1}/(y_{n}x_{n-1}+1),$; $y_{n+1}=y_{n-1}/(x_{n}y_{n-1}+1)$, Math. Comput. Modelling, 53 (2011), 1261–1267.
