Analysis of the Van der Pol oscillator containing derivatives of fractional order

Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Vinagre, B. M.; Calderón, A. J.

http://hdl.handle.net/10400.22/4576

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Authors

Barbosa, Ramiro S.

Machado, J. A. Tenreiro

Vinagre, B. M.

Calderón, A. J.

Abstract(s)

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.