ANALYSIS OF THE LIMIT CYCLE OF A GENERALISED VAN DER POL EQUATION BY A TIME TRANSFORMATION METHOD

DOI10.1080/16073606.1994.9631770zbMath0807.34037OpenAlexW1984692918MaRDI QIDQ4312329

D. P. Mason, G. M. Moremedi

Publication date: 9 November 1994

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/16073606.1994.9631770

zbMATH Keywords

method of multiple scaleslimit cyclenumerical solutiongeneralized van der Pol equationtime transformation perturbation method

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Singular perturbations for ordinary differential equations (34E15) Numerical analysis in abstract spaces (65J99)

Cites Work

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• On perturbation procedure for limit cycle analysis
• Phase portraits and bifurcations of the non-linear oscillator: \(x+(\alpha+\gamma x^ 2)x'+\beta x+\delta x^ 3=0\)
• Non-linear oscillator limit cycle analysis using a time transformation approach
• The method of matched asymptotic expansions for the periodic solution of the Van der Pol equation
• On the limit cycle of a generalized van der Pol equation
• Solutions to van der Pol's equation using a perturbation method
• Analysis of forced non-linear undamped oscillators by a time transformation method
• Analysis of non-linear autonomous conservative oscillators by a time transformation method
• On the amplitude decay of strongly non-linear damped oscillators
• Perturbation Analysis of the Limit Cycle of the Free van der Pol Equation
• Analytical Theory of Nonlinear Oscillations. IV: The Periodic Oscillations of the Equation $x - \varepsilon ( {1 - x^{2n + 2} } )x + x^{2n + 1} = \varepsilon a\cos \omega t$, $a > 0$, $\omega > 0$ Independent of $\varepsilon $

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