On a (2,2)-rational recursive sequence

Abstract

We investigate the asymptotic behavior of the recursive difference equation y_n+1 = (α+βy _n )/(1+y_n-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 y_n+1 = (a + by _n )/(A + By_n-1), when the parameters a, b, A, B ∈ ℝ and abAB ≠ 0.