Dynamics of the fractional-order Van der Pol oscillator

In this paper we propose a modified version of the classical unforced Van der Pol oscillator that occurs when introducing a fractional-order time derivative in the state space equations that describes its dynamics. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, for several values of order´s fractional derivative and, consequently, of the total system order. It is shown that the system can exhibit different output behavior depending on the total system order. Several numerical simulations and performance indices illustrate the fractional dynamics