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On a (2,2)-rational recursive sequence

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Abstract

We investigate the asymptotic behavior of the recursive difference equation yn+1 = (α+βy n )/(1+yn-1) when the parameters α < 0 and β . 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 + by n )/(A + Byn-1), when the parameters a, b, A, B and abAB ≠ 0.

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Correspondence to Mohamed Ben Rhouma.

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