Opuscula Mathematica
Opuscula Math. 43, no. 2 (2023), 131-143

Global attractivity of a higher order nonlinear difference equation with unimodal terms

Abdulaziz Almaslokh
Chuanxi Qian
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.
Mathematics Subject Classification: 39A10, 92D25.
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About the authors ▼
Abdulaziz Almaslokh
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
Chuanxi Qian (corresponding author)
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, MS 39762, USA
About the article ▼
Communicated by Stevo Stević.
Received: 2022-12-13.
Revised: 2023-01-03.
Accepted: 2023-01-06.
Published online: 2023-03-27.
Cite this article as ▼
Abdulaziz Almaslokh, Chuanxi Qian, Global attractivity of a higher order nonlinear difference equation with unimodal terms, Opuscula Math. 43, no. 2 (2023), 131-143, https://doi.org/10.7494/OpMath.2023.43.2.131.
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