The Lyapunov exponents of the Van der Pol oscillator

Lyapunov exponents characterize the dynamics of a system near its attractor. For the Van der Pol oscillator these are quantities for which an approximation should be at hand. Similar to the asymptotic approximation of amplitude and period, expressions are derived for the non‐zero Lyapunov exponent f...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2005-07, Vol.28 (10), p.1131-1139
Main Authors: Grasman, Johan, Verhulst, Ferdinand, Shih, Shagi-Di
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
limit-cycle
Lyapunov exponents
Mathematical analysis
Mathematics
Ordinary differential equations
relaxation oscillation
Sciences and techniques of general use
series
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Van der Pol oscillator
vanderpol equation
weakly oscillation
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Summary:Lyapunov exponents characterize the dynamics of a system near its attractor. For the Van der Pol oscillator these are quantities for which an approximation should be at hand. Similar to the asymptotic approximation of amplitude and period, expressions are derived for the non‐zero Lyapunov exponent for both small and large parameter values. Copyright © 2005 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.606