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Global behavior of positive solutions of a third order difference equations system | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 249، دوره 14، شماره 1، فروردین 2023، صفحه 3189-3200 اصل مقاله (453.48 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28701.3970 | ||
| نویسنده | ||
| Phong Nam Mai* | ||
| Department of Mathematical Analysis, University of Transport and Communications, Hanoi, Vietnam | ||
| تاریخ دریافت: 23 مهر 1401، تاریخ بازنگری: 14 دی 1401، تاریخ پذیرش: 22 دی 1401 | ||
| چکیده | ||
| In this paper, we investigate the global behavior of positive solutions of the system of difference equations \begin{equation*} x_{n+1}=\alpha+ \dfrac{y^p_{n}}{y^p_{n-2}},\ y_{n+1}=\alpha+ \dfrac{x^q_{n} }{x^q_{n-2}}, \ n=0, 1, 2, ... \end{equation*} where parameters $\alpha, p, q \in (0, \infty)$ and the initial values $x_{i}$, $y_{i}$ are arbitrary positive numbers for $ i= -2,-1, 0$. Moreover, the rate of convergence of positive solutions is established and some numerical examples are given to demonstrate our theoretical results. | ||
| کلیدواژهها | ||
| Difference equation؛ semi-cycle؛ equilibrium؛ boundedness؛ global asymptotic stability؛ rate of convergence | ||
| مراجع | ||
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