Research Article
Boundedness Character of the System of Recursive Difference Equations
Abstract
In this paper, we take into consideration the boundedness character of positive solutions of the difference system
$x_{n}=\alpha +\prod \limits_{i=1}^{k}y_{n-i}^{a_{i}} $
$y_{n}=\beta +\prod \limits_{i=1}^{k}x_{n-i}^{b_{i}},$
where $a_{i},b_{i}\in \mathbb{R}$, $i=\overline{1,k},$ $a_{k}\neq 0,$ $b_{k}\neq 0$ and $\alpha $ and $\beta $ are nonnegative real numbers.
References
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- El-Dessoky, M.M., Elsayed, E.M. On the solutions and periodic nature of some systems of rational difference equations, J. of Comp. Anal. App., 18(2)(2015), 206–218.
- El-Metwally, H., Yalcinkaya, I., Cinar,.C., Global stability of an economic model, Utilitas Mathematica, 95(2014), 235–244.
- Elsayed, E.M., The expressions of solutions and periodicity for some nonlinear systems of rational difference equations, Advanced Studies in Cont. Math., 25(3)(2015), 345–371.
- Elsayed, E.M., On the solutions and periodic nature of some systems of difference equations, International J. of Biomath., 7(6)(2014).
- Elsayed, E.M., Cinar, C., On the solutions of some systems of difference equations, Utilitas Mathematica, 93(2014), 279–289.
- Elsayed, E.M., Ibrahim, T.F. Periodicity and solutions for some systems of nonlinear rational difference equations, Hacettepe J. of Math. and Statis., 44(6)(2015,) 1361–1390.
- Ergin, S., Karatas, R., On the dynamics of a recursive sequence, ARS Combinatoria, 109(2013), 353–360.
- Gelisken, A., Kara, M.,Some general systems of rational Difference Equations, J. of Dif. Eq., 2015(2015).
- Gelisken, A., Cinar, C., Yalcinkaya, I., On a max-type difference equation, Advances in Dif. Eq., 2010(2010).
- Gelisken, A., Cinar,C., Kurbanli, A.S., On the asymptotic behavior and periodic nature of a difference equation with maximum, Comp. & Math. with App., 59(2)(2010), 898–902.
- Gelisken, A., Cinar, C., On the global attractivity of a max-type difference equation, Disc. Dyn. Nat. Soc., 2009(2009).
- Halim, Y., Touafek,N., Yazlik, Y., Dynamic behavior of a second-order nonlinear rational difference equation, Turkish Journal of Mathematics, 39(2015), 1004–1018.
- Hatir, E., Mansour, T., Yalcinkaya, I., On a fuzzy difference equation, Utilitas Mathematica, 93(2014), 135–151.
- Iricanin, B.,On a higher-order nonlinear diffrence equation, Abstr. Appl. Anal., 2010(2010).
- Karatas, R., Global behavior of a higher order difference equation, Comp. & Math. with App., 60(3)(2010), 830–839.
- Karatas, R., Global behavior of a rational recursive sequence, Ars Combinatoria, 97(A)(2010), 421–428.
- Kurbanli, A.S., Cinar, C., Yalcinkaya, I., 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. and Comp. Model., 53(5-6)(2011), 1261–1267.
- Papaschinopoulos, G., Radin, M., Schinas, C.J., Study of the asymptotic behavior of the solutions of three systems of difference equations of exponential form, Appl. Math. Comput., 218(2012), 5310–5318.
- Papaschinopoulos, G., Schinas, C.J., Stefanidou, G., On the nonautonomous difference equation $x_{n+1}=A_{n}+(x_{n-1}^{p}/x_{n}^{q}),$ Appl. Math. Comput., 217(2011), 5573–5580.
- Simsek, D., Demir, B., Cinar, C., On the solutions of the system of difference equations $x_{n+1}=\max\{A/x_{n},y_{n}/x_{n}\}$, $y_{n+1}=\max\{A/y_{n},x_{n}/y_{n}\}$, 2009(2009).
- Simsek, D., Cinar, C., Yalcinkaya, I., On the recursive sequence $x(n+1)=x(n-(5k+9))/(1+x(n-4)x(n-9)...x(n-(5k+4)))$, Taiwanese J. of Math., 12(5)(2008), 1087–1099.
- Stefanidou, G., Papaschinopoulos, G., Schinas, C.J., On a system of two exponential type difference equations, Commun. Appl. Nonlinear Anal., 17(2)(2010), 1-13.
- Stevic,S., Alghamdi, M.A., Alotaibi, A., Boundedness character of the recursive sequence $x_{n}=\alpha +\prod\limits_{j=1}^{k}x_{n-j}^{a_{j}}$, Applied Mathematics Letters, 50(2015), 83–90.
- Stevic, S., On the recursive sequence $x_{n+1}=\alpha+(x_{n-1}^{p}/x_{n}^{p})$, J. Appl. Math. Comput., 18 (1-2)(2005), 229–234.
- Stevic, S., On the recursive sequence $x_{n+1}=A+(x_{n}^{p}/x_{n-1}^{r})$, Discrete Dyn. Nat. Soc., 2007(2007).
- Stevic, S., On a class of higher-order difference equations,Chaos Solutions Fractals, 42(2009), 138–145.
- Tollu, D.T., Yazlik, Y., Taskara, N., On fourteen solvable systems of difference equations, Appl. Math. Comput., 233(2014), 310–319.
- Touafek, N., Elsayed, E.M., On a second order rational systems of difference equations, Hokkaido Mathematical Journal, 44(1)(2015), 29–45.
- Yalcinkaya, I., On the global asymptotic behavior of a system of two nonlinear difference equations, ARS Combinatoria, 95(2010), 151–159.
- Yazlik, Y., Tollu, D.T., Taskara, N., On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences, 38(17)(2015), 4388–4410.
- Yazlik, Y., Tollu, D.T. Taskara, N., On the behaviour of solutions for some systems of difference equations, J. of Comp. Anal. App., 18(1)(2015), 166–178.
- Yazlik, Y., Elsayed, E.M., Taskara, N., On the behaviour of the solutions of difference equation systems, J. of Comp. Anal. App., 16(5)(2014), 932–941.
Abstract
References
- Alzahrani, E.O., El-Dessoky, M.M., Elsayed, E.M., Kuang,Y., Solutions and properties of some degenerate systems of difference equations, J. of Comp. Anal. App., 18(2)(2015), 321–333.
- El-Dessoky, M.M., Elsayed, E.M. On the solutions and periodic nature of some systems of rational difference equations, J. of Comp. Anal. App., 18(2)(2015), 206–218.
- El-Metwally, H., Yalcinkaya, I., Cinar,.C., Global stability of an economic model, Utilitas Mathematica, 95(2014), 235–244.
- Elsayed, E.M., The expressions of solutions and periodicity for some nonlinear systems of rational difference equations, Advanced Studies in Cont. Math., 25(3)(2015), 345–371.
- Elsayed, E.M., On the solutions and periodic nature of some systems of difference equations, International J. of Biomath., 7(6)(2014).
- Elsayed, E.M., Cinar, C., On the solutions of some systems of difference equations, Utilitas Mathematica, 93(2014), 279–289.
- Elsayed, E.M., Ibrahim, T.F. Periodicity and solutions for some systems of nonlinear rational difference equations, Hacettepe J. of Math. and Statis., 44(6)(2015,) 1361–1390.
- Ergin, S., Karatas, R., On the dynamics of a recursive sequence, ARS Combinatoria, 109(2013), 353–360.
- Gelisken, A., Kara, M.,Some general systems of rational Difference Equations, J. of Dif. Eq., 2015(2015).
- Gelisken, A., Cinar, C., Yalcinkaya, I., On a max-type difference equation, Advances in Dif. Eq., 2010(2010).
- Gelisken, A., Cinar,C., Kurbanli, A.S., On the asymptotic behavior and periodic nature of a difference equation with maximum, Comp. & Math. with App., 59(2)(2010), 898–902.
- Gelisken, A., Cinar, C., On the global attractivity of a max-type difference equation, Disc. Dyn. Nat. Soc., 2009(2009).
- Halim, Y., Touafek,N., Yazlik, Y., Dynamic behavior of a second-order nonlinear rational difference equation, Turkish Journal of Mathematics, 39(2015), 1004–1018.
- Hatir, E., Mansour, T., Yalcinkaya, I., On a fuzzy difference equation, Utilitas Mathematica, 93(2014), 135–151.
- Iricanin, B.,On a higher-order nonlinear diffrence equation, Abstr. Appl. Anal., 2010(2010).
- Karatas, R., Global behavior of a higher order difference equation, Comp. & Math. with App., 60(3)(2010), 830–839.
- Karatas, R., Global behavior of a rational recursive sequence, Ars Combinatoria, 97(A)(2010), 421–428.
- Kurbanli, A.S., Cinar, C., Yalcinkaya, I., 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. and Comp. Model., 53(5-6)(2011), 1261–1267.
- Papaschinopoulos, G., Radin, M., Schinas, C.J., Study of the asymptotic behavior of the solutions of three systems of difference equations of exponential form, Appl. Math. Comput., 218(2012), 5310–5318.
- Papaschinopoulos, G., Schinas, C.J., Stefanidou, G., On the nonautonomous difference equation $x_{n+1}=A_{n}+(x_{n-1}^{p}/x_{n}^{q}),$ Appl. Math. Comput., 217(2011), 5573–5580.
- Simsek, D., Demir, B., Cinar, C., On the solutions of the system of difference equations $x_{n+1}=\max\{A/x_{n},y_{n}/x_{n}\}$, $y_{n+1}=\max\{A/y_{n},x_{n}/y_{n}\}$, 2009(2009).
- Simsek, D., Cinar, C., Yalcinkaya, I., On the recursive sequence $x(n+1)=x(n-(5k+9))/(1+x(n-4)x(n-9)...x(n-(5k+4)))$, Taiwanese J. of Math., 12(5)(2008), 1087–1099.
- Stefanidou, G., Papaschinopoulos, G., Schinas, C.J., On a system of two exponential type difference equations, Commun. Appl. Nonlinear Anal., 17(2)(2010), 1-13.
- Stevic,S., Alghamdi, M.A., Alotaibi, A., Boundedness character of the recursive sequence $x_{n}=\alpha +\prod\limits_{j=1}^{k}x_{n-j}^{a_{j}}$, Applied Mathematics Letters, 50(2015), 83–90.
- Stevic, S., On the recursive sequence $x_{n+1}=\alpha+(x_{n-1}^{p}/x_{n}^{p})$, J. Appl. Math. Comput., 18 (1-2)(2005), 229–234.
- Stevic, S., On the recursive sequence $x_{n+1}=A+(x_{n}^{p}/x_{n-1}^{r})$, Discrete Dyn. Nat. Soc., 2007(2007).
- Stevic, S., On a class of higher-order difference equations,Chaos Solutions Fractals, 42(2009), 138–145.
- Tollu, D.T., Yazlik, Y., Taskara, N., On fourteen solvable systems of difference equations, Appl. Math. Comput., 233(2014), 310–319.
- Touafek, N., Elsayed, E.M., On a second order rational systems of difference equations, Hokkaido Mathematical Journal, 44(1)(2015), 29–45.
- Yalcinkaya, I., On the global asymptotic behavior of a system of two nonlinear difference equations, ARS Combinatoria, 95(2010), 151–159.
- Yazlik, Y., Tollu, D.T., Taskara, N., On the solutions of a max-type difference equation system, Mathematical Methods in the Applied Sciences, 38(17)(2015), 4388–4410.
- Yazlik, Y., Tollu, D.T. Taskara, N., On the behaviour of solutions for some systems of difference equations, J. of Comp. Anal. App., 18(1)(2015), 166–178.
- Yazlik, Y., Elsayed, E.M., Taskara, N., On the behaviour of the solutions of difference equation systems, J. of Comp. Anal. App., 16(5)(2014), 932–941.
There are 33 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | June 30, 2024 |
| Published in Issue | Year 2024 Volume: 16 Issue: 1 |