Numerical simulation of van der Pol equation using multiple scales modified Lindstedt-Poincaré method

DOI10.1007/s40010-019-00655-yzbMath1490.65135OpenAlexW3004042621MaRDI QIDQ2052241

Yanyan Li

Publication date: 25 November 2021

Published in: Proceedings of the National Academy of Sciences, India. Section A. Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40010-019-00655-y

zbMATH Keywords

van der Pol equationmultiple scales methodperturbation problemsmodified Lindstedt-Poincaré method

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (1)

Multiple Time-Scales Dynamics of a Cardiac Pacemaker Model with Application to Heart Rhythm Modeling: Theoretical Study and FPGA Implementation

Uses Software

• Matlab

Cites Work

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• A homotopy analysis method for limit cycle of the van der Pol oscillator with delayed amplitude limiting
• A novel harmonic balance analysis for the van der Pol oscillator
• Methods for solving singular perturbation problems arising in science and engineering
• Construction of approximate periodic solutions to a modified van der Pol oscillator
• A new perturbation algorithm with better convergence properties: multiple scales Lindstedt Poincaré method
• Non-linear oscillator limit cycle analysis using a time transformation approach
• A modified Lindstedt-Poincaré method for certain strongly non-linear oscillators
• The method of matched asymptotic expansions for the periodic solution of the Van der Pol equation
• Solutions to van der Pol's equation using a perturbation method
• On a problem of modified Lindstedt--Poincaré for certain strongly nonlinear oscillators
• Perturbation procedure for the Van der Pol oscillator based on the Hopf bifurcation theorem
• Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order
• A geometric approach to two-timing
• VAN DER POL'S OSCILLATOR UNDER DELAYED FEEDBACK

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