Integrable Duffing's maps and solutions of the Duffing equation

DOI10.1016/S0960-0779(02)00089-9zbMath1031.37047OpenAlexW2007633277MaRDI QIDQ1419129

D. Massart

Publication date: 14 January 2004

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(02)00089-9

zbMATH Keywords

periodic orbitsintegrable mappingsdiscrete soliton system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Forced motions for nonlinear problems in mechanics (70K40) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28)

Related Items (14)

Bifurcations of periodic orbits in Duffing equation with periodic damping and external excitations ⋮ Bifurcations and chaos in three-well Duffing system with one external forcing ⋮ On exact discretization of cubic-quintic Duffing oscillator ⋮ Bifurcations and chaos in Duffing equation with damping and external excitations ⋮ Bifurcations and Chaos in the Duffing Equation with Parametric Excitation and Single External Forcing ⋮ Global periodic structure of integrable Duffing's maps. ⋮ Complex dynamics in three-well Duffing system with two external forcings ⋮ An improvement to the homotopy perturbation method for solving nonlinear Duffing's equations ⋮ Bifurcations and chaos in Duffing equation ⋮ Numerical solution of Duffing equation by the Laplace decomposition algorithm ⋮ Discretization of Hamiltonian systems and intersection theory ⋮ Duffing Oscillator and Elliptic Curve Cryptography ⋮ HIGH-DIMENSIONAL CHAOS IN DISSIPATIVE AND DRIVEN DYNAMICAL SYSTEMS ⋮ Complex dynamics in Duffing-Van der Pol equation

Cites Work

• On integrable mappings of standard type
• On integrability and chaos in discrete systems
• Advanced synergetics. Instability hierarchies of self-organizing systems and devices
• Iteration of some discretizations of the nonlinear Schrödinger equation
• Regular and chaotic dynamics.
• Global periodic structure of integrable hyperbolic map
• Global periodic structure of integrable Duffing's maps.
• Integrable mappings and soliton equations
• Integrable mappings and soliton equations. II
• Exact solution of a difference approximation to Duffing's equation
• Best difference equation approximation to Duffing's equation
• The inverse scattering transform: Semi-infinite interval
• A Nonlinear Difference Scheme and Inverse Scattering
• Discrete versions of the Painlevé equations
• Do integrable mappings have the Painlevé property?
• Perspectives of Nonlinear Dynamics

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