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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 | ||
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