Global asymptotic stability of a second order rational difference equation

The main goal of this paper is to investigate the global asymptotic stability of the difference equationyn+1=pn+ynpn+yn-1,n=0,1,2,…,wherepn=α,ifnis evenβ,ifnis oddandα>0,β>0,α≠βand the initial conditions y-1,y0∈[0,∞)y-1,y0∈[0,∞) . We show that the unique equilibrium y¯=1 is globally asymptotically stable under the certain conditions.