Study of the Van der Pol Oscillator with Fractional Derivatives

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

http://hdl.handle.net/10400.22/13246

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Authors

Barbosa, Ramiro

Tenreiro Machado, J. A.

Vinagre, B. M.

Calderón, A. J.

Abstract(s)

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.