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More details on analysis of fractional-order Van der Pol oscillator

Tavazoei, M. S ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1177/1077546308096101
  3. Publisher: 2009
  4. Abstract:
  5. 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. © 2009 SAGE Publications
  6. Keywords:
  7. Stability ; Analytical results ; Fractional order ; Fractional order system ; Fractional-order systems ; Fractional-order Van der Pol oscillator ; Integer order ; Integer-order counterparts ; Limit set ; Numerical simulation ; Oscillation ; Undamped oscillators ; Van der Pol oscillator ; Van Der Pol systems ; Automobile exhibitions ; Circuit oscillations ; Lyapunov methods ; Oscillators (mechanical) ; System stability
  8. Source: JVC/Journal of Vibration and Control ; Volume 15, Issue 6 , 2009 , Pages 803-819 ; 10775463 (ISSN)
  9. URL: https://journals.sagepub.com/doi/abs/10.1177/1077546308096101