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On a (2,2)-rational recursive sequence

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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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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

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