Global attractivity in a recursive sequence
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Publication:702617
DOI10.1016/j.amc.2003.10.007zbMath1063.39011OpenAlexW1997948744MaRDI QIDQ702617
David J. Evans, Bill Chen, Graham M. Megson, Xiaofan Yang
Publication date: 17 January 2005
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2003.10.007
global attractivityrecursive sequenceexponential convergencelocal asymptotic stabilityrational difference equationinvariant intervalsoscillatory behaviorsemicycleequilibria stability
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Related Items (11)
On the recursive sequence \( {x}_{n+1}=\frac{x_{n-\left(4k+3\right)}}{1+\prod_{t=0}^2{x}_{n-\left(k+1\right)t-k}} \) ⋮ On the difference equation \(x_{n+1}= \frac{px_{n-s} + x_{n-t}}{qx_{n-s} + x_{n-t}}\) ⋮ On the recursive sequence xn+1 = xn-7/1+xn-3 ⋮ A solution form of a class of higher-order rational difference equations ⋮ On the recursive sequence \(x_{n+1}=(\alpha-\beta x_{n-k})/g(x_n,x_{n-1},\dots,x_{n-k+1})\) ⋮ Note on a rational system of \((4k+4)\)-order difference equations: periodic solution and convergence ⋮ Unnamed Item ⋮ On the dynamics of the recursive sequence \(x_{n+1}=\frac{\alpha x_{n-1}}{\beta+\gamma\sum_{k=1}^tx_{n-2k}\prod_{k=1}^tx_{n-2k}}\) ⋮ On the recursive sequence \( {x}_{n+1}=\frac{x_{n-\left(k+1\right)}}{1+{x}_n{x}_{n-1}\dots {x}_{n-k}} \) ⋮ On the recursive sequence \(x_n = \frac{ax_{n-1}+bx_{n-2}}{c+dx_{n-1}x_{n-2}}\) ⋮ On the dynamics of the recursive sequence \(x_{n+1}=\frac{x_{n-1}}{\beta+\gamma x^2_{n-2}x_{n-4}+\gamma x_{n-2}x^2_{n-4}}\)
Cites Work
- Global asymptotic stability in a rational recursive sequence
- On the recursive sequence \(x_{n+1}=\alpha+x_{n-1}/x_n\)
- Global attractivity in the recursive sequence \(x_{n+1}=(\alpha-\beta x_{n})/(\gamma-x_{n-1})\)
- Global attractivity in a rational recursive sequence.
- On the recursive sequences \(x_{n+1}=\frac {-\alpha x_{n-1}}{\beta\pm x_n}\)
- On asymptotic behaviour of the difference equation \(x_{x+1}=\alpha + \frac {x_{n-k}}{x_n}\)
- On the recursive sequence \(x_{n+1} = \frac{\alpha+\beta x_{n}+\gamma x_{n-1}} {Bx_{n}+Cx_{n-1}}\)
- Global stability of \(y_{n+1}=A+\frac{y_n}{y_{n-k}}\)
- A note on the periodic cycle of \(x_{n+2}=(1+x_{n+1})/(x_n)\)
- On the recursive sequence \(y_{n+1}=(p+y_{n-1})/(qy_n+y_{n-1})\)
- On the recursive sequence \(x_{n+1}=\frac{\alpha+\beta x_n}{Bx_n+Cx_{n-1}}\).
- Stability properties of nonlinear difference equations and conditions for boundedness
- On rational recursive sequences
- Stability of the recursive sequence \(x_{n+1}=(\alpha-\beta x_n)/(\gamma+x_{n-1})\)
- A rational recursive sequence
- A rational difference equation
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