TY - JOUR
ID - 6599
TI - Dynamics of a system of higher order difference equations with a period-two coefficient
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Oudina, Sihem
AU - Kerker, Mohamed Amine
AU - Salmi, Abdelouahab
AD - Laboratory of Applied Mathematics, Badji Mokhtar-Annaba University, P.O. Box 12, Annaba, 23000, Algeria
Y1 - 2022
PY - 2022
VL - 13
IS - 2
SP - 2043
EP - 2058
KW - system of difference equations
KW - Periodic solutions
KW - Global asymptotic stability
KW - boundedness
DO - 10.22075/ijnaa.2022.26716.3398
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_6599.html
L1 - https://ijnaa.semnan.ac.ir/article_6599_4fe4678b05671565a9016b279531c3a7.pdf
ER -