Global behavior of positive solutions of a third order difference equations system

	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
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
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