The global attractivity of a higher order rational difference equation

This paper studies global asymptotic stability for positive solutions to the equation yn = y(n-k)y(n-1)y(n-m) + y(n-k) + y(n-1) + y(n-m)/1 + y(n-k)y(n-1) + y(n-k)y(n-m) + y(n-1)y(n-m), n = 0, 1, ..., with y(-m), y(-m+1) ,..., y(-1) is an element of (0, infinity) and 1 <= k < 1 < m. The paper also includes a listing of possible semi-cycle structures for various (k, 1, m). The results generalize several others in the recent literature. (c) 2006 Published by Elsevier Inc.