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Journal of Vibration and Control
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More Details on Analysis of Fractional-order Van der Pol Oscillator

Mohammad S. Tavazoei

Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

Mohammad Haeri

Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran, haeri{at}sina.sharif.edu

Mina Attari

Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

Sadegh Bolouki

Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

Milad Siami

Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

This paper is devoted to the analysis of fractional order Van der Pol system studied in the literature. Based on the existing theorems on the stability of incommensurate fractional order systems, we determine parametric range for which a fractional order Van der Pol system with a specific order can perform as an undamped oscillator. Numerical simulations are presented to support the given analytical results. These results also illuminate a main difference between oscillations in a fractional order Van der Pol oscillator and its integer order counterpart. We show that contrary to integer order case, trajectories in a fractional Van der Pol oscillator do not converge to a unique cycle.

Key Words: Fractional order system • fractional-order Van der Pol oscillator • stability • oscillation • limit set.

This version was published on June 1, 2009

Journal of Vibration and Control, Vol. 15, No. 6, 803-819 (2009)
DOI: 10.1177/1077546308096101
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