Boundedness and Global Attractivity of a Higher‐Order Nonlinear Difference Equation

Abstract

We investigate the local stability, prime period‐two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn+1 = (r + pyn + yn−k)/(qyn + yn−k), n ∈ ℕ0, where the parameters p, q, r ∈ (0, ∞), k ∈ {1, 2, 3, …} and the initial conditions y−k, …, y0 ∈ (0, ∞). We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.