On the difference equation yn+1=A+ynyn-k with A < 0

摘要

We find conditions for the global asymptotic stability of the unique negative equilibrium y¯=1+A of the equation(0.1)yn+1=A+ynyn-k,where y−k, y−k+1, … , y0 ∈ (0, ∞), A < 0 and k ∈ {1, 2, 3, 4, …}.