Global asymptotic behavior of a rational difference equation

The main goal of this paper is to investigate the global asymptotic behavior of the difference equation:yn+1=yn-1pn+yn,n=0,1,2,…where {pn} is a period-two sequence:pn=α,ifnis evenβ,ifnis oddwith α,β∈(0,∞) and the initial conditions y-1,y0∈[0,∞). We obtain some global attractivity results for the equilibrium of this system for different values of the parameters.