Journal
JOURNAL OF VIBRATION AND CONTROL
Volume 13, Issue 9-10, Pages 1291-1301Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1077546307077463
Keywords
fractional calculus; Van der Pol oscillator; nonlinear oscillators; fractional order operators
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In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.
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