The global attractivity of a higher order rational difference equation

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