On the dynamics of the nonlinear rational difference equation \(x_{n+1}=Ax_{n}+Bx_{n-k}+Cx_{n-l}+\frac{bx_{n-k}}{dx{n-k}-ex{n-1}}\)
DOI10.1016/j.joems.2014.11.002zbMath1328.39002OpenAlexW2073796560MaRDI QIDQ900495
M. A. El-Moneam, Elsayed M. E. Zayed
Publication date: 22 December 2015
Published in: Journal of the Egyptian Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.joems.2014.11.002
global stabilityglobal attractordifference equationsboundedness characterprime period two solutionlocally asymptotically stable
Qualitative theory for ordinary differential equations (34C99) Additive difference equations (39A10) Stability theory for difference equations (39A30)
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Cites Work
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- On the rational recursive sequence \(X_{N+1}=\gamma X_{N-K}+(AX_N+BX_{N-K})/(CX_N-DX_{N-K})\)
- On the rational recursive sequence \(x_{n+1}=\frac{A+\alpha_0x_n+\alpha_1x_{n-\sigma}}{B+\beta_0x_n+\beta_1x_{n-\tau}}\)
- On the dynamics of the recursive sequence \(x_{n+1}=\frac{x_{n-1}}{\beta+\gamma x^2_{n-2}x_{n-4}+\gamma x_{n-2}x^2_{n-4}}\)
- 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 rational recursive sequence \(x_{n+1}=\frac {\alpha x_n+\beta x_{n-1}+\gamma x_{n-2}+\delta x_{n-3}} {Ax_b+ Bx_{n-1}+ Cx_{n-2}+ Dx_{n-3}}\)
- Dynamics of a higher order rational difference equation
- On the rational recursive sequence \(x_{n+1}=Ax_{n}+Bx_{n-k}+\frac{\beta x_{n}+\gamma x_{n-k}}{cx_{n}+Dx_{n-k}}\)
- On the asymptotic stability of \(x_{n+1}=(a+x_nx_{n - k})/(x_n+x_{n - k})\)
- On the rational recursive sequence \(x_{n+1}=\frac{\alpha + \beta x_{n-k}}{\gamma-x_{n}}\)
- On the global attractivity of two nonlinear difference equations
- On the rational recursive two sequences \(x_{n+1}=ax_{n-k}+bx_{n-k}/(cx_n+\delta dx_{n-k})\)
- On the difference equation \(x_{n+1}=ax_n-bx_n/(cx_n-dx_{n-1})\)
- On the rational recursive sequence $ x_{n+1}=\dfrac {\alpha_0x_n+\alpha_1x_{n-l}+\alpha _2x_{n-k}} {\beta_0x_n+\beta_1x_{n-l}+\beta_2x_{n-k}}$
- On the rational recursive sequence $ \ x_{n+1}=\Big ( A+\sum _{i=0}^k\alpha _ix_{n-i}\Big ) \Big / \sum _{i=0}^k\beta _ix_{n-i} $
- Dynamics of a rational difference equation
- A rational difference equation
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