Dynamics of a system of higher order difference equations with a period-two coefficient
نویسندگان
1 Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria
2 Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria
3 Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria
doi
10.22075/ijnaa.2022.26716.3398چکیده
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.
