@Article{Almaslokh2023,
author = "Almaslokh, Abdulaziz and Qian, Chuanxi",
title = "Global attractivity of a higher order nonlinear difference equation with unimodal terms",
journal = "Opuscula Math.",
year = "2023",
volume = "43",
number = "2",
pages = "131--143",
doi = "https://doi.org/10.7494/OpMath.2023.43.2.131",
url = "https://doi.org/10.7494/OpMath.2023.43.2.131",
abstract = "In the present paper, we study the asymptotic behavior of the following higher order nonlinear difference equation with unimodal terms \[x(n+1)= ax(n)+ bx(n)g(x(n)) + cx(n-k)g(x(n-k)), \quad n=0, 1, \ldots,\] where \(a\), \(b\) and \(c\) are constants with \(0\lt a\lt 1\), \(0\leq b\lt 1\), \(0\leq c \lt 1\) and \(a+b+c=1\), \(g\in C[[0, \infty), [0, \infty)]\) is decreasing, and \(k\) is a positive integer. We obtain some new sufficient conditions for the global attractivity of positive solutions of the equation. Applications to some population models are also given.",
keywords = "higher order difference equation, positive equilibrium, unimodal term, global attractivity, population model",
issn = "1232-9274"
}