پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شمارهها | 678 |
| تعداد مقالات | 9,883 |
| تعداد مشاهده مقاله | 70,049,399 |
| تعداد دریافت فایل اصل مقاله | 49,322,230 |
On the dynamics of a nonautonomous rational difference equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 17، دوره 12، شماره 1، مرداد 2021، صفحه 203-213 اصل مقاله (521.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.4760 | ||
| نویسندگان | ||
| Mohamed Amine Kerker* ؛ Elbahi Hadidi؛ Abdelouahab Salmi | ||
| Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria | ||
| تاریخ دریافت: 17 مرداد 1399، تاریخ بازنگری: 01 دی 1399، تاریخ پذیرش: 05 دی 1399 | ||
| چکیده | ||
| In this paper, we study the following nonautonomous rational difference equation \[ y_{n+1}=\frac{\alpha_n+y_n}{\alpha_n+y_{n-k}},\quad n=0,1,..., \] where $\left\{\alpha_n\right\}_{n\geq0}$ is a bounded sequence of positive numbers, $k$ is a positive integer and the initial values $y_{-k},...,y_0$ are positive real numbers. We give sufficient conditions under which the unique equilibrium $\bar{y}=1$ is globally asymptotically stable. Furthermore, we establish an oscillation result for positive solutions about the equilibrium point. Our work generalizes and improves earlier results in the literature. | ||
| کلیدواژهها | ||
| nonautonomous difference equation؛ global asymptotic stability؛ oscillation | ||
| مراجع | ||
|
[1] R. Abo-Zeid, Global behavior of a higher order rational difference equation, Filomat 30(12) (2016) 3265–3276. [2] M. Abu Alhalawa and M. Saleh, Dynamics of higher order rational difference equation xn+1 =α+βxn/A+Bxn+Cxn−k, Int. J. Nonlinear Anal. Appl. 8(2) (2017) 363–379. [3] E. Chatterjee and S. Hassan, On the asymptotic character of a generalized rational difference equation, Dis. Cont. Dyn. Sys. A 38 (2018) 1707–1718. [4] I. Dekkar, N. Touafek and Q. Din, On the global dynamics of a rational difference equation with periodic coefficients, J. Appl. Math. Comput. 60(1) (2019) 567–588. [5] S. Elaydi, An Introduction to Difference Equations, Undergraduate Texts in Mathematics, Springer, New York, 2005. [6] M. Gumus and R. Abo-Zeid, On the solutions of a (2k + 2)th order difference equation, Dyn. Contin. Discrete Impuls Syst. Ser. B Appl. Algorithms 25 (2018) 129–143. [7] M. G¨um¨us and R. Abo-Zeid, Global behavior of a rational second order difference equation, J. Appl. Math. Comput. 62(1) (2020) 119–133. [8] T. F. Ibrahim and N. Touafek, On a third order rational difference equation with variable coefficients, Dyn. Contin. Discrete Impuls Syst. Ser. B Appl. Algorithms 20 (2013) 251–264. [9] A. Jafar and M. Saleh, Dynamics of nonlinear difference equation xn+1 =βxn+γxn−k/A+Bxn+Cxn−k, J. Appl. Math. Comput. 57(1-2) (2018) 493–522. [10] M.A. Kerker, E. Hadidi, and A. Salmi, Qualitative behavior of a higher-order nonautonomous rational difference equation, J. Appl. Math. Comput. 64 (2020) 399–409. [11] V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Academic Publishers, Dordrecht, 1993. [12] V. L. Kocic, G. Ladas, and L. W. Rodrigues, On rational recursive sequences, J. Math. Anal. Appl. 173 (1993)127–157. [13] V. Lakshmikantham and D. Trigiante, Theory of Difference Equations, Numerical Methods and Applications, Marcel Dekker, Inc., New York, 2002. [14] P. Liu, C. Wang, Y. Li and R. Li, Asymptotic behavior of equilibrium point for a system of fourth-order rational difference equations, J. Comput. Anal. Appl. 27 (2019) 947–961. [15] C. Qian and J. Smith, On quasi-periodic solutions of forced higher order nonlinear difference equations, Electron.J. Qual. Theory Differ. Equ. 2020(2020) 20. Id/No 6. [16] M. Saleh, N. Alkoumi and A. Farhat, On the dynamics of a rational difference equation xn+1 =α+βxn+γxn−k /Bxn+Cxn−k, Chaos Solitons Fractals 96 (2017) 76–84. [17] M. Saleh and A. Farhat, Global asymptotic stability of the higher order equation xn+1 =axn+bxn−k/A+Bxn−k, J. Appl. Math. Comput. 55(1-2) (2017) 135–148. [18] N. Touafek, On a second order rational difference equation, Hacet. J. Math. Stat. 41 (2012) 867–874. [19] C. Wang, S. Wang and W. Wang, Global asymptotic stability of equilibrium point for a family of rational difference equations, Appl. Math. Lett. 24 (2011) 714–718. | ||
|
آمار تعداد مشاهده مقاله: 15,871 تعداد دریافت فایل اصل مقاله: 7,888 |
||