Global attractivity of the equilibrium of a difference equation: An elementary proof assisted by computer algebra system

DOI10.1080/10236190902932718zbMath1216.39022arXiv0812.3398OpenAlexW1969708564MaRDI QIDQ3085087

Orlando Merino

Publication date: 28 March 2011

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

Full work available at URL: https://arxiv.org/abs/0812.3398

zbMATH Keywords

global attractivityequilibriumrational second order difference equation

Mathematics Subject Classification ID

Multiplicative and other generalized difference equations (39A20) Stability theory for difference equations (39A30)

Related Items (10)

Global stability and bifurcations of perturbed Gumowski–Mira difference equation ⋮ Global behavior of solutions of the generalized Lyness difference equations under quadratic perturbations ⋮ Global asymptotic stability of a generalization of the Pielou difference equation ⋮ Unconditional convergence of difference equations ⋮ Basin of attraction through invariant curves and dominant functions ⋮ Unnamed Item ⋮ A general method for studying quadratic perturbations of the third-order Lyness difference 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 ⋮ Local stability implies global stability for the 2-dimensional Ricker map ⋮ Asymptotic behavior results for solutions to some nonlinear difference equations

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Global stability, two conjectures and Maple
• The global attractivity of difference equations of nonincreasing nonlinearities with applications.
• Invariants and related Liapunov functions for difference equations
• The dynamics of \(x_{n+1}= \frac {\alpha + \beta x_n}{A+Bx_n+Cx_{n-1}}\) facts and conjectures
• Global stability for a class of difference equation
• On rational recursive sequences
• Open problems and conjectures
• Open problems and conjectures
• The Y2K problem revisited

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