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

Almaslokh Abdulaziz, Qian Chuanxi

Opuscula Mathematica

2023

Vol. 43, no. 2

131--143

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.

Asymptotic behaviour of solutions of higher order difference equations

Migda M.

Demonstratio Mathematica

1998

Vol. 31, nr 1

71-80