Nonlinear time transformation method for strong nonlinear oscillation systems

DOI10.1007/BF02489252zbMath0769.34027OpenAlexW2324993299MaRDI QIDQ4034323

Zhao Xu

Publication date: 16 May 1993

Published in: Acta Mechanica Sinica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02489252

zbMATH Keywords

nonlinear oscillationsvan der Pol equationforced oscillationsnonlinear time transformation methodLindstedt- Poincaré method

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (4)

Predicting homoclinic and heteroclinic bifurcation of generalized Duffing-harmonic-van der Pol oscillator ⋮ A new perturbation procedure for limit cycle analysis in three-dimensional nonlinear autonomous dynamical systems ⋮ Homoclinic and heteroclinic solutions of cubic strongly nonlinear autonomous oscillators by the hyperbolic perturbation method ⋮ Approximation of limit cycles in two-dimensional nonlinear systems near a Hopf bifurcation by canonical transformations

Cites Work

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• Non-linear oscillator limit cycle analysis using a time transformation approach
• Construction of approximate analytical solutions to a new class of non-linear oscillator equations
• Perturbation procedure for the Van der Pol oscillator based on the Hopf bifurcation theorem
• An extension of the Van der Pol oscillator

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