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Study of the Van der Pol Oscillator with Fractional Derivatives

By Ramiro Barbosa, J. A. Tenreiro Machado, B. M. Vinagre and A. J. Calderón


In this paper we propose a modified version of the classical Van der Pol oscillator by 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, by using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes by using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.N/

Topics: Van der Pol oscillator, Fractional-order, Fractional-order operators
Year: 2006
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