Global behavior of solutions of the generalized Lyness difference equations under quadratic perturbations

DOI10.1016/j.amc.2015.03.006zbMath1390.39038OpenAlexW2056959785MaRDI QIDQ1636879

Yun Zhang, Guifeng Deng, Fengjie Geng

Publication date: 7 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.amc.2015.03.006

zbMATH Keywords

Lyapunov functionperturbationglobal asymptotic stabilitybifurcation point

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)

Cites Work

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• Global behavior of solutions to two classes of second-order rational difference equations
• Results and conjectures about order \(q\) Lyness' difference equation \(u_{n+q}u_n=a+u_{n+q - 1}+ \dots +u_{n+1}\) in \(\mathbb R_{\ast}^+\), with a particular study of the case \(q=3\)
• Periodic solutions of the Lyness max equation.
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• Invariants and related Liapunov functions for difference equations
• Some invariants for \(k\)th-order Lyness equation.
• Results and problems about solutions of perturbed Lyness' type orderkdifference equations in , with examples, and test of the efficiency of a quasi-Lyapunov function method
• On 2- and 3-periodic Lyness difference equations
• Global attractivity of the equilibrium of a difference equation: An elementary proof assisted by computer algebra system
• Global behaviour of solutions of cyclic systems ofqorder 2 or 3 generalized Lyness' difference equations and of other more general equations of higher order

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