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.


70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics
70K40 Forced motions for nonlinear problems in mechanics
26A33 Fractional derivatives and integrals
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