Advances in Difference Equations
Volume 2005 (2005), Issue 3, Pages 319-332
doi:10.1155/ADE.2005.319
On a (2,2)-rational recursive sequence
Mohamed Ben Rhouma
, M.A. El-Sayed
and Azza K. Khalifa
Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Muscat 123 Al-Khodh, Oman
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.