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

SAGE Publications - Tập 13 Số 9-10 - Trang 1291-1301 - 2007
Ramiro S. Barbosa1, J. A. Tenreiro Machado1, Blas M. Vinagre2, Antonio José Calderón2
1Institute of Engineering of Porto, Rua Dr. António Bernardino de Almeida 431, 4200-072 Porto, Portugal
2Escuela de Ingenierías Industriales, Universidad de Extremadura, Badajoz, Spain

Tóm tắt

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.

Từ khóa


Tài liệu tham khảo

10.1016/S0960-0779(02)00438-1

10.1142/4507

Barbosa, R.S., Proceedings of the IEEE International Conference on Computational Cybernetics(ICCC'04)

10.1109/9.159595

Hartley, T.T., 1995, Theory and Applications, 42, 485

10.1142/3779

10.1109/9.995039

Machado, J.A.T., 2001, Fractional Calculus & Applied Analysis, 4, 47

10.1016/j.chaos.2003.12.039

10.1006/jsvi.2001.4172

10.1006/jsvi.2002.5170

Oldham, K.B., 1974, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order

Oustaloup, A., 1995, La Dérivation Non Entière: Théorie, Synthèse et Applications

Pereira, E., Proceedings of the First IFAC Workshop on Fractional Differentiation and Its Applications (FDA'04)

Podlubny, I., 1999, Fractional Differential Equations

Vinagre, B.M., 2000, Fractional Calculus & Applied Analysis, 3, 231

Thông tin
Thông tin xuất bản

SAGE Publications

Tập 13 Số 9-10

1291-1301

Thông tin tác giả