The global attractivity of a higher order rational difference equation

Abstract

This paper studies global asymptotic stability for positive solutions to the equation y n = y n − k y n − l y n − m + y n − k + y n − l + y n − m 1 + y n − k y n − l + y n − k y n − m + y n − l y n − 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.