پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 610 |
| تعداد مقالات | 9,028 |
| تعداد مشاهده مقاله | 67,082,840 |
| تعداد دریافت فایل اصل مقاله | 7,656,343 |
Dynamics of a system of higher order difference equations with a period-two coefficient | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 164، دوره 13، شماره 2، مهر 2022، صفحه 2043-2058 اصل مقاله (525.07 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.26716.3398 | ||
| نویسندگان | ||
| Sihem Oudina؛ Mohamed Amine Kerker* ؛ Abdelouahab Salmi | ||
| Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria | ||
| تاریخ دریافت: 09 فروردین 1401، تاریخ بازنگری: 21 اردیبهشت 1401، تاریخ پذیرش: 18 خرداد 1401 | ||
| چکیده | ||
| The aim of this paper is to study the dynamics of the system of two rational difference equations: $$ x_{n+1}=\alpha_{n}+\frac{y_{n-k}}{y_{n}},\quad y_{n+1}=\alpha_{n}+\frac{x_{n-k}}{x_{n}},\quad n=0, 1,\dots $$ where \(\left\{\alpha_n\right\}_{n\geq0}\) is a two periodic sequence of nonnegative real numbers and the initial conditions \(x_{i}, y_{i}\) are arbitrary positive numbers for \(i=-k, -k+1, -k+2,\dots, 0\) and $k\in\mathbb{N}$. We investigate the boundedness character of positive solutions. In addition, we establish some sufficient conditions under which the local asymptotic stability and the global asymptotic stability are assured. Furthermore, we determine the rate of the convergence of the solutions. Some numerical are considered in order to confirm our theoretical results. | ||
| کلیدواژه‌ها | ||
| System of difference equations؛ Periodic solutions؛ Global asymptotic stability؛ Boundedness | ||
| مراجع | ||
|
[1] A. Abo-Zeid, Global behavior and oscillation of a third order difference equation, Quaest. Math. 44 (2022), no. 9, 1261–1280. [2] S. Abulrub and M. Aloqeili, Dynamics of the system of difference equations xn+1 = A + yn−k yn , yn+1 = B + xn−k xn , Qual. Theory Dyn. Syst. no. 19 (2020), 19–69. [3] E. Camouzis and G. Ladas, Dynamics of third order rational difference equations with open problems and conjecture advances in discrete mathematics and applications, Chapman & Hall/CRC, Boca Raton, 2008. [4] E. Camouzis and G. Papaschinopoulos, Global asymptotic behavior of positive solutions on the system of rational difference equations xn+1 = 1 + xn yn−m , yn+1 = 1 + yn xn−m , Appl. Math. Lett. 17 (2004), no. 6, 733–737. [5] I. Dekkar, N. Touafek and Y. Yazlik, Global stability of a third-order nonlinear system of difference equations with period-two coefficients, RACSAM 111 (2017), 325–347. [6] S. Elaydi, An introduction to difference equations, undergraduate texts in mathematics, Springer, New York, 2005. [7] M. G¨um¨us, The global asymptotic stability of a system of difference equations, J. Differ. Equ. Appl. 24 (2018), no. 6, 976–991. [8] M. G¨um¨us and R. Abo-Zeid, Global behavior of a rational second order difference equation, J. Appl. Math. Comput. 62 (2020), no. 1, 119–133. [9] O. Ocalan, Dynamics of difference equation xn+1 = pn+ xn−k xn with a period-two coefficient, Appl. Math. Comput. 228 (2014), 31–37. [10] G. Papaschinopoulos, On the system of two difference equations xn+1 = A + xn−1 yn , yn+1 = A + yn−1 xn , Int. J. Math. Sci. 23 (2000), 839–848. [11] G. Papaschinopoulos, C.J. Schinas and G. Stefanidou, On the nonautonomous difference equation xn+1 = An + x p n−1 x q n , Appl. Math. Comput. 217 (2011), 5573–5580. [12] M. Pituk, More on Poincare’s and Perron’s theorems for difference equations, J. Difference Equ. Appl. 8 (2002), no. 3, 201–216. [13] 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 Fract. 96 (2017), 76–84. [14] D. Zhang, W. Ji, L. Wang and X. Li. On the symmetrical system of rational difference equations xn+1 = A + yn−k yn , yn+1 = A + xn−k xn , Appl. Math. 4 (2013), 834–837. [15] Q. Zhang, W. Zhang, Y. Shao and J. Liu, On the system of high order rational difference equations, Int. Scholarly Res. Not. 2014 (2014), 1–5. [16] Q. Zhang, L. Yang and J. Liu, On the recursive system xn+1 = A + xn−m yn , yn+1 = A + yn−m xn , Act Math. Univ. Comenianae 82 (2013), no. 2, 201–208. | ||
|
آمار تعداد مشاهده مقاله: 44,058 تعداد دریافت فایل اصل مقاله: 355 |
||