Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order-Reference-Cited by-同舟云学术

Analysis of the Van der Pol Oscillator Containing Derivatives of Fractional Order

Published:2007-09 Issue:9-10 Volume:13 Page:1291-1301
ISSN:1077-5463
Container-title:Journal of Vibration and Control
language:en
Short-container-title:Journal of Vibration and Control

Author:

Barbosa Ramiro S.¹,Machado J.A. Tenreiro²,Vinagre B.M.³,Calderón A.J.³

Affiliation:

1. Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal

2. Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal,

3. Escuela de Ingenierías Industriales, Universidad de Extremadura, Badajoz, Spain

Abstract

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the 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.

Publisher

SAGE Publications

Subject

Mechanical Engineering,Mechanics of Materials,Aerospace Engineering,Automotive Engineering,General Materials Science

Link

http://journals.sagepub.com/doi/pdf/10.1177/1077546307077463

Reference16 articles.

1. Chaos in fractional-order autonomous nonlinear systems

2. Nonlinear Noninteger Order Circuits and Systems — An Introduction

3. Fractal system as represented by singularity function

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