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Analysis of the van der Pol oscillator containing derivatives of fractional order. (English) Zbl 1158.70009
Summary: We propose a modified version of the classical van der Pol oscillator, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order van der Pol oscillator is analyzed in 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.
70K05Phase plane analysis, limit cycles (general mechanics)
70K50Transition to stochasticity (general mechanics)
70K40Forced nonlinear motions (general mechanics)
26A33Fractional derivatives and integrals (real functions)