Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order | Zendy

Ramiro S. Barbosa | Zendy; J. A. Tenreiro Machado | Zendy; Blas M. Vinagre | Zendy; Antonio José Calderón | Zendy

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Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order

Author(s) -

Ramiro S. Barbosa,

J. A. Tenreiro Machado,

Blas M. Vinagre,

Antonio José Calderón

Publication year - 2007

Publication title -

journal of vibration and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.734

H-Index - 68

eISSN - 1741-2986

pISSN - 1077-5463

DOI - 10.1177/1077546307077463

Subject(s) - van der pol oscillator , fractional calculus , phase portrait , mathematics , order (exchange) , bifurcation , mathematical physics , mathematical analysis , physics , nonlinear system , quantum mechanics , finance , economics

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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