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

DOI10.1007/s10440-009-9545-yzbMath1204.39008OpenAlexW2008914198MaRDI QIDQ983686

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

Publication date: 24 July 2010

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/38133

zbMATH Keywords

boundednessglobal stabilityglobal attractorrational difference equationslocal asymptotic stabilityprime period two solution

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 (9)

Unnamed Item ⋮ On the period-two cycles of \(x_{n + 1} = (\alpha + \beta x_n + \gamma x_{n - k})/(A + Bx_n + Cx_{n - k})\) ⋮ On the dynamics of the nonlinear rational difference equation \(x_{n+1}=Ax_{n}+Bx_{n-k}+Cx_{n-l}+\frac{bx_{n-k}}{dx{n-k}-ex{n-1}}\) ⋮ On the difference equation \(x_{n+1}=ax_{n-l}+bx_{n-k}+f ( x_{n-l},x_{n-k} )\) ⋮ Unnamed Item ⋮ The periodicity and solutions of the rational difference equation with periodic coefficients ⋮ Unnamed Item ⋮ Analytic solutions and stability of sixth order difference equations ⋮ 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

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• On the rational recursive sequence \(x_{n+1}=\frac {\alpha x_n+\beta x_{n-1}+\gamma x_{n-2}+\delta x_{n-3}} {Ax_b+ Bx_{n-1}+ Cx_{n-2}+ Dx_{n-3}}\)
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• On the recursive sequence 𝑥_{𝑛+1}=\frac{𝐴}𝑥_{𝑛}+\frac{1}𝑥_{𝑛-2}
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• Open problems and conjectures
• Stability of the recursive sequence \(x_{n+1}=(\alpha-\beta x_n)/(\gamma+x_{n-1})\)
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