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- Title
GLOBAL ATTRACTIVITY OF A HIGHER ORDER NONLINEAR DIFFERENCE EQUATION WITH UNIMODAL TERMS.
- Authors
Almaslokh, Abdulaziz; 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)), n = 0, 1, . . ., where a, b and c are constants with 0 < a < 1, 0 ≤ b < 1, 0 ≤ c < 1 and a + b + c = 1, g ∈ C[[0,∞), [0,∞)] 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.
- Subjects
NONLINEAR difference equations; DIFFERENCE equations
- Publication
Opuscula Mathematica, 2023, Vol 43, Issue 2, p131
- ISSN
1232-9274
- Publication type
Article
- DOI
10.7494/OpMath.2023.43.2.131