Dynamics of the fractional-order Van der Pol oscillator

Ramiro S. Barbosa, J. A T Machado, Isabel M. Ferreira, J. Tar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

17 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings
EditorsW. Elmenreich, W. Haidinger, J.A.T. Machado
Pages373-378
Number of pages6
Publication statusPublished - 2004
EventICCC 2004 - Second IEEE International Conference on Computational Cybernetics - Vienna, Austria
Duration: Aug 30 2004Sep 1 2004

Other

OtherICCC 2004 - Second IEEE International Conference on Computational Cybernetics
CountryAustria
CityVienna
Period8/30/049/1/04

Fingerprint

Derivatives
Computer simulation

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Barbosa, R. S., Machado, J. A. T., Ferreira, I. M., & Tar, J. (2004). Dynamics of the fractional-order Van der Pol oscillator. In W. Elmenreich, W. Haidinger, & J. A. T. Machado (Eds.), ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings (pp. 373-378)

Dynamics of the fractional-order Van der Pol oscillator. / Barbosa, Ramiro S.; Machado, J. A T; Ferreira, Isabel M.; Tar, J.

ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings. ed. / W. Elmenreich; W. Haidinger; J.A.T. Machado. 2004. p. 373-378.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Barbosa, RS, Machado, JAT, Ferreira, IM & Tar, J 2004, Dynamics of the fractional-order Van der Pol oscillator. in W Elmenreich, W Haidinger & JAT Machado (eds), ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings. pp. 373-378, ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Vienna, Austria, 8/30/04.
Barbosa RS, Machado JAT, Ferreira IM, Tar J. Dynamics of the fractional-order Van der Pol oscillator. In Elmenreich W, Haidinger W, Machado JAT, editors, ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings. 2004. p. 373-378
Barbosa, Ramiro S. ; Machado, J. A T ; Ferreira, Isabel M. ; Tar, J. / Dynamics of the fractional-order Van der Pol oscillator. ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings. editor / W. Elmenreich ; W. Haidinger ; J.A.T. Machado. 2004. pp. 373-378
@inproceedings{21c2c44124224118b5907c640a35035c,
title = "Dynamics of the fractional-order Van der Pol oscillator",
abstract = "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.",
author = "Barbosa, {Ramiro S.} and Machado, {J. A T} and Ferreira, {Isabel M.} and J. Tar",
year = "2004",
language = "English",
isbn = "0780385888",
pages = "373--378",
editor = "W. Elmenreich and W. Haidinger and J.A.T. Machado",
booktitle = "ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings",

}

TY - GEN

T1 - Dynamics of the fractional-order Van der Pol oscillator

AU - Barbosa, Ramiro S.

AU - Machado, J. A T

AU - Ferreira, Isabel M.

AU - Tar, J.

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=20844431533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20844431533&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:20844431533

SN - 0780385888

SP - 373

EP - 378

BT - ICCC 2004 - Second IEEE International Conference on Computational Cybernetics, Proceedings

A2 - Elmenreich, W.

A2 - Haidinger, W.

A2 - Machado, J.A.T.

ER -