On a (2,2)-rational recursive sequence

Abstract

We investigate the asymptotic behavior of the recursive difference equation yn+1=(α+βyn)/(1+yn−1) when the parameters α<0 and β∈ℝ. In particular, we establish the boundedness and the global stability of solutions for different ranges of the parameters α and β. We also give a summary of results and open questions on the more general recursive sequences yn+1=(a+byn)/(A+Byn−1), when the parameters a,b,A,B∈ℝ and abAB≠0.