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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.
MSC:
70K05Phase plane analysis, limit cycles (general mechanics)
70K50Transition to stochasticity (general mechanics)
70K40Forced nonlinear motions (general mechanics)
26A33Fractional derivatives and integrals (real functions)