The global attractivity of the rational difference equation yn = frac(yn - k + yn - m, 1 + yn - k yn - m)

Abstract

This paper studies global asymptotic stability for positive solutions to the equation yn = frac(yn - k + yn - m, 1 + yn - k yn - m), n = 0, 1, ..., with y- m, y- m + 1, ..., y- 1 ∈ (0, ∞) and 1 ≤ k < m. The paper includes a discussion of stability for a wide class of symmetric rational difference equations which includes the type studied here as well as several other in the recent literature.