A novel harmonic balance analysis for the Van Der Pol oscillator

Liping Liu; Earl. H. Dowell; Kenneth C. Hall

doi:10.1016/j.ijnonlinmec.2006.09.004

A novel harmonic balance analysis for the Van Der Pol oscillator

Liping Liu
, Earl. H. Dowell
, Kenneth C. Hall

Mathematics and Statistics

University of Texas Pan American
Duke University

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

51 Scopus citations

Abstract

This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge-Kutta) methods. © 2007 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	2-12
Number of pages	11
Journal	International Journal of Non-Linear Mechanics
Volume	42
Issue number	1
DOIs	https://doi.org/10.1016/j.ijnonlinmec.2006.09.004
State	Published - Jan 1 2007

Keywords

Chaos
Dynamical systems
Harmonic balance method
Limit cycle oscillations
Van der Pol's oscillator

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10.1016/j.ijnonlinmec.2006.09.004

Cite this

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title = "A novel harmonic balance analysis for the Van Der Pol oscillator",

abstract = "This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge-Kutta) methods. {\textcopyright} 2007 Elsevier Ltd. All rights reserved.",

keywords = "Chaos, Dynamical systems, Harmonic balance method, Limit cycle oscillations, Van der Pol's oscillator",

author = "Liping Liu and Dowell, \{Earl. H.\} and Hall, \{Kenneth C.\}",

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N2 - This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge-Kutta) methods. © 2007 Elsevier Ltd. All rights reserved.

AB - This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge-Kutta) methods. © 2007 Elsevier Ltd. All rights reserved.

KW - Chaos

KW - Dynamical systems

KW - Harmonic balance method

KW - Limit cycle oscillations

KW - Van der Pol's oscillator

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JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

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A novel harmonic balance analysis for the Van Der Pol oscillator

Abstract

Keywords

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