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

DOI10.1007/S12190-008-0205-6zbMath1181.39014OpenAlexW2069316841MaRDI QIDQ1034965

M. A. El-Moneam, Elsayed M. E. Zayed

Publication date: 9 November 2009

Published in: Journal of Applied Mathematics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12190-008-0205-6

zbMATH Keywords

boundednessperiodicityasymptotic stabilityglobal attractorbasinrational difference equation

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Growth, boundedness, comparison of solutions to difference equations (39A22) Periodic solutions of difference equations (39A23) Stability theory for difference equations (39A30)

Related Items (4)

Unnamed Item ⋮ On the dynamics of the nonlinear rational difference equation \(x_{n+1}=Ax_{n}+Bx_{n-k}+Cx_{n-l}+\frac{bx_{n-k}}{dx{n-k}-ex{n-1}}\) ⋮ Unnamed Item ⋮ On the rational difference equation y n + 1 = α 0 y n + α 1 y n − p + α 2 y n − q + α 3 y n − r + α 4 y n − s β 0 y n + β 1 y n − p + β 2 y n − q + β 3 y n − r + β 4 y n − s

Cites Work

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• On the rational recursive sequence \(x_{n+1}=\frac {\alpha x_n+\beta x_{n-1}+\gamma x_{n-2}+\delta x_{n-3}} {Ax_b+ Bx_{n-1}+ Cx_{n-2}+ Dx_{n-3}}\)
• On the rational recursive sequence \(x_{n+1}=(A+\sum_{i=0}^{k}\alpha _{i}x_{n - i})/(B+\sum _{i=0}^{k}\beta _{i}x_{n - i})\)
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• A Note on the Difference Equation x n +1 = ∑ i =0 k α i x n − i p i
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• On the Recursive Sequencex_n+1=α+ (βx_n−1)/(1 +g(x_n))
• Asymptotic behavior of a sequence defined by iteration with applications
• Stability of the recursive sequence \(x_{n+1}=(\alpha-\beta x_n)/(\gamma+x_{n-1})\)
• A global convergence result with applications to periodic solutions

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