Global stability and bifurcations of perturbed Gumowski–Mira difference equation

DOI10.1080/10236198.2015.1045892zbMath1330.39018OpenAlexW1786448862MaRDI QIDQ3448512

Guifeng Deng, Fengjie Geng

Publication date: 26 October 2015

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

Full work available at URL: https://doi.org/10.1080/10236198.2015.1045892

zbMATH Keywords

Lyapunov functionperturbationasymptotic stabilitybifurcationperiodic solutionrational difference equationGumowski-Mira system

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Periodic solutions of difference equations (39A23) Stability theory for difference equations (39A30) Bifurcation theory for difference equations (39A28)

Related Items (2)

Dichotomy between a generalized Lyness difference equation with period-two coefficients and its perturbation ⋮ Global behavior of a generalized Lyness difference equation under linear perturbation

Cites Work

• Stability of the Gumowski-Mira equation with period-two coefficient
• A general method for studying quadratic perturbations of the third-order Lyness difference equation
• On the algebraic difference equations \(u_{n+2}+u_{n}=\psi (u_{n+1})\) in \(\mathbb R\), related to a family of elliptic quartics in the plane
• Global behavior of solutions to two classes of second-order rational difference equations
• Recurrences and discrete dynamic systems
• Global asymptotic stability for two recursive difference equations.
• Invariants and related Liapunov functions for difference equations
• 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
• Global attractivity of the equilibrium of a difference equation: An elementary proof assisted by computer algebra system
• PERIOD-DOUBLING BIFURCATIONS FOR SYSTEMS OF DIFFERENCE EQUATIONS AND APPLICATIONS TO MODELS IN POPULATION BIOLOGY
• NONAUTONOMOUS TWO-PERIODIC GUMOVSKI–MIRA DIFFERENCE EQUATIONS
• BIFURCATIONS OF STABLE SETS IN NONINVERTIBLE PLANAR MAPS
• Bifurcations in a second-order difference equation from macroeconomics†Supported by NSFC, TRAPOYT and MOE Research grants.

This page was built for publication: Global stability and bifurcations of perturbed Gumowski–Mira difference equation