Invariants and related Liapunov functions for difference equations

DOI10.1016/S0893-9659(00)00068-9zbMath0958.39021OpenAlexW1976888212MaRDI QIDQ1586305

Mustafa R. S. Kulenović

Publication date: 13 November 2000

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0893-9659(00)00068-9

zbMATH Keywords

stabilityinvariantsLyapunov functionsnonlinear difference equationsGumovski-Mira equationLyness' equationTodd's equation

Mathematics Subject Classification ID

Related Items (28)

Birkhoff normal forms, KAM theory and time reversal symmetry for certain rational map ⋮ Dichotomy of a perturbed Lyness difference equation ⋮ Global stability and bifurcations of perturbed Gumowski–Mira difference equation ⋮ Global behavior of solutions of the generalized Lyness difference equations under quadratic perturbations ⋮ STABILITY OF THE kTH ORDER LYNESS' EQUATION WITH A PERIOD-k COEFFICIENT ⋮ 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 ⋮ Stability analysis of a certain class of difference equations by using KAM theory ⋮ Stability, periodicity, and symmetries of certain second-order fractional difference equation with quadratic terms via KAM theory ⋮ DYNAMICS OF SOME RATIONAL DISCRETE DYNAMICAL SYSTEMS VIA INVARIANTS ⋮ Global behavior of certain nonautonomous linearizable three term difference equations ⋮ Global asymptotical stability of the coexistence fixed point of a Ricker-type competitive model ⋮ A general method for studying quadratic perturbations of the third-order Lyness difference equation ⋮ Studying discrete dynamical systems through differential equations ⋮ Short Notes: Invariants: A Functional-equation Approach ⋮ Dynamics of the third order Lyness' difference equation ⋮ Attractivity and global stability for linearizable difference equations ⋮ Some invariants for \(k\)th-order Lyness equation. ⋮ On second-order rational difference equations, part 1 ⋮ Stability of the Gumowski-Mira equation with period-two coefficient ⋮ On second-order rational difference equations, Part 2 ⋮ On third-order rational difference equations, part 1 ⋮ Global attractivity of the equilibrium of a difference equation: An elementary proof assisted by computer algebra system ⋮ Global behavior of solutions to two classes of second-order rational difference equations ⋮ Global periodicity and complete integrability of discrete dynamical systems ⋮ The dynamics of \(x_{n+1}= \frac {\alpha + \beta x_n}{A+Bx_n+Cx_{n-1}}\) facts and conjectures ⋮ Global asymptotical stability of the positive equilibrium of a logistic competitive model ⋮ Invariants and Liapunov functions for nonautonomous systems ⋮ Semiconjugates of One-dimensional Maps

Cites Work

• Recurrences and discrete dynamic systems
• Invariants for some rational recursive sequences with periodic coefficients
• A note on unbounded solutions of a class of second order rational difference equations
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