The symmetrical Van der Pol oscillator

B. Z. Kaplan; Y. Horen

doi:10.7227/IJEEE.39.2.5

The symmetrical Van der Pol oscillator

B. Z. Kaplan, Y. Horen

Department of Electrical & Computer Engineering

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The limit cycle is associated in the Van der Pol oscillator with damping introduced to merely one of its state equations. In the present oscillator nonlinear damping is added to both equations. A unique behaviour is observed in spite of the smallness of the departure from the Van der Pol case. The present treatment is due to classical Poincaré-Bendixson and Liapunov methods. It illuminates in a surprisingly simple and elegant manner the great power of the methods.

Original language	English
Pages (from-to)	128-137
Number of pages	10
Journal	International Journal of Electrical Engineering and Education
Volume	39
Issue number	2
DOIs	https://doi.org/10.7227/IJEEE.39.2.5
State	Published - 1 Jan 2002

Keywords

Liapunov
Limit cycle
Oscillator
Poincaré-Bendixson
Rayleigh
Van der Pol

ASJC Scopus subject areas

Education
Electrical and Electronic Engineering

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AB - The limit cycle is associated in the Van der Pol oscillator with damping introduced to merely one of its state equations. In the present oscillator nonlinear damping is added to both equations. A unique behaviour is observed in spite of the smallness of the departure from the Van der Pol case. The present treatment is due to classical Poincaré-Bendixson and Liapunov methods. It illuminates in a surprisingly simple and elegant manner the great power of the methods.

KW - Liapunov

KW - Limit cycle

KW - Oscillator

KW - Poincaré-Bendixson

KW - Rayleigh

KW - Van der Pol

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ER -

The symmetrical Van der Pol oscillator

Abstract

Keywords

ASJC Scopus subject areas

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