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On a (2,2)-rational recursive sequence
Advances in Difference Equations volume 2005, Article number: 415435 (2005)
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 ∈ 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 + by n )/(A + Byn-1), when the parameters a, b, A, B ∈ ℝ and abAB ≠ 0.
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Ben Rhouma, M., El-Sayed, M.A. & Khalifa, A.K. On a (2,2)-rational recursive sequence. Adv Differ Equ 2005, 415435 (2005). https://doi.org/10.1155/ADE.2005.319