On the rational recursive sequence \(x_{n+1}=(\alpha - \beta x_{n})/(\gamma - \delta x_{n} - x_{n - k})\)

DOI10.1155/2008/391265zbMath1154.39017OpenAlexW1964892854WikidataQ58644750 ScholiaQ58644750MaRDI QIDQ938534

Taher A. Nofal, Ali B. Shamardan, Elsayed M. E. Zayed

Publication date: 19 August 2008

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2008/391265

zbMATH Keywords

periodic solutionglobal attractorglobal asymptotic stabilitybounded solutionpositive equilibriumrational difference equation

Mathematics Subject Classification ID

Related Items (1)

On the recursive sequence \(x_{n+1}=(\alpha-\beta x_{n-k})/g(x_n,x_{n-1},\dots,x_{n-k+1})\)

Cites Work

• Global attractivity in a second-order nonlinear difference equation
• The asymptotic stability of \(x_{n+1}-ax_ n+bx_{n-k}=0\)
• A note on the periodic cycle of \(x_{n+2}=(1+x_{n+1})/(x_n)\)
• On the recursive sequence \(x_{n+1}= -1/x_n+ A/x_{n-1}\)
• The dynamics of \(x_{n+1}= \frac {\alpha + \beta x_n}{A+Bx_n+Cx_{n-1}}\) facts and conjectures
• The recursive sequence \(x_{n+1} = g(x_{n},x_{n-1})/(A + x_{n})\)
• Global behavior of \(y_{n+1}=\frac{p+y_{n-k}}{qy_n+y_{n-k}}\).
• On rational recursive sequences
• On the Dynamics of
• On the recursive sequence
• On the Trichotomy Character of x n +1 =(α+β x n +γ x n −1 )/( A + x n )
• Open problems and conjectures
• Stability of the recursive sequence \(x_{n+1}=(\alpha-\beta x_n)/(\gamma+x_{n-1})\)

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