Duffing-van der Pol type oscillator

Authors

Guangyue Gao, University of Texas-Pan American

Date of Award

7-2010

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Zhaosheng Feng

Second Advisor

Dr. Barnabas Bede

Third Advisor

Dr. Paul Bracken

Abstract

The nonlinear Duffing-van der Pol oscillator system is studied by means of the Lie symmetry reduction method and the Preller-Singer method. With the particular case of coefficients, this system has physical relevance as a simple model in certain flow-induced structural vibration problems. Under certain parametric conditions, we are concerned with the first integrals of the Duffing-van der Pol oscillator system. After making a series of variable transformations, we apply the Preller-Singer method and the Lie symmetry reduction method to obtain the first integrals of the simplified equations without complicated calculations.

Comments

Copyright 2010 Guangyue Gao. All Rights Reserved.

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Granting Institution

University of Texas-Pan American