Duffing-van der Pol-type nonlinear oscillator system

Authors

Jing Cui, University of Texas-Pan American

Date of Award

5-2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Zhaosheng Feng

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Paul Bracken

Abstract

In this thesis, we are concerned with the nonlinear Duffing–van der Pol–type oscillator system by means of the Lie symmetry reduction method. This system has physical relevance as a simple model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. By applying the Lie symmetry analysis, we find two nontrivial infinitesimal generators, and use them to construct canonical variables. Through the inverse analysis, some dynamical properties of the nonlinear system under certain parametric conditions are presented. Comparison with the existing results by the Prelle– Singer procedure is provided.

Comments

Copyright 2011 Jing Cui. All Rights Reserved.

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Granting Institution

University of Texas-Pan American