Asymptotic behavior of a nonlinear difference equation

Abstract

In this note we investigate the asymptotic behavior of the solutions of the difference equation x n+1 = f (x n , x n-1 , ..., x n-k+1 ), n≥k - 1, with initial conditions x 0 , x 1 , ..., x k-1 ∈ [0, ∞), where the function f satisfies certain additional conditions. The main result in this note apply to some classes of mathematical biology models, for example: Generalized Beddington-Holt stock recruitment model, Flour beetle population model and Mosquito population equations.