A general method for studying quadratic perturbations of the third-order Lyness difference equation

DOI10.1186/1687-1847-2013-193zbMath1381.39013OpenAlexW2146834657WikidataQ59301227 ScholiaQ59301227MaRDI QIDQ681134

Guifeng Deng, Nianzu Liu, Qiuying Lu

Publication date: 30 January 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2013-193

zbMATH Keywords

Lyapunov functionglobal asymptotic stabilitybifurcation pointfirst integraldifference equationLyness equationquadratic perturbations

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Growth, boundedness, comparison of solutions to difference equations (39A22) Stability theory for difference equations (39A30) Bifurcation theory for difference equations (39A28)

Related Items (2)

Global stability and bifurcations of perturbed Gumowski–Mira difference equation ⋮ Global behavior of solutions of the generalized Lyness difference equations under quadratic perturbations

Cites Work

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• Zeeman's monotonicity conjecture
• Periodic solutions of the Lyness max equation.
• Periodicity and strict oscillation for generalized Lyness equations
• Invariants and related Liapunov functions for difference equations
• Some invariants for \(k\)th-order Lyness equation.
• 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
• Global Behavior of the Solutions of Lyness' Difference Equation
• Dynamics of the third order Lyness' difference equation

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