Dynamics of a higher order nonlinear rational difference equation

DOI10.1080/10236190512331319352zbMath1071.39017OpenAlexW1965266823MaRDI QIDQ4663091

Stevo Stević, Wang-Tong Li, You-Hui Su

Publication date: 30 March 2005

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236190512331319352

zbMATH Keywords

periodic solutionglobal attractorglobal asymptotical stabilityinvariant intervaloscillation periodic solution

Mathematics Subject Classification ID

Discrete version of topics in analysis (39A12) Multiplicative and other generalized difference equations (39A20)

Related Items

Degenerate Neimark–Sacker bifurcation of a second-order rational difference equation, Global asymptotic stability for a higher order nonlinear rational difference equations, Global dynamics for a higher-order rational difference equation, Global asymptotic stability of a second order rational difference equation, Unconditional convergence of difference equations, Global asymptotical stability of a second order rational difference equation, Global stability of a rational difference equation, Global attractivity of a higher order nonlinear difference equation, Dynamics of a rational difference equation, Global stability of a rational difference equation, Boundedness and global attractivity of a higher-order nonlinear difference equation, Global attractivity of a higher-order nonlinear difference equation, Global behavior of \(x_{n + 1} = (\alpha + \beta x_{n - k}) /(\gamma + x_n)\), When does local asymptotic stability imply global attractivity in rational equations?

Cites Work

• Global attractivity in the recursive sequence \(x_{n+1}=(\alpha-\beta x_{n})/(\gamma-x_{n-1})\)
• Global attractivity in a rational recursive sequence.
• Global attractivity for a class of higher order nonlinear difference equations.
• Global stability of \(y_{n+1}=A+\frac{y_n}{y_{n-k}}\)
• 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 \(y_{n+1}=\frac{p+y_{n-k}}{qy_n+y_{n-k}}\).
• A Note on the Difference Equation x n +1 = ∑ i =0 k α i x n − i p i
• Asymptotic behavior of a sequence defined by iteration with applications
• Periodic Character of a Class of Difference Equation
• Global attractivity in a nonlinear second‐order difference equation