Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 73849, 6 pages
doi:10.1155/2007/73849

Dynamics of a class of higher order difference equations

Abstract

We prove that all positive solutions of the autonomous difference equation xn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, where k,m∈ℕ, and f is a continuous function satisfying the condition β min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um} for some β∈(0,1), converge to the positive equilibrium x¯=(α−1)/(β+1) if α>1.