The First-Integral Method for Duffing-Van Der Pol-Type Oscillator System

Authors

Xiaochuan Hu, University of Texas-Pan American

Date of Award

8-2011

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Zhaosheng Feng

Second Advisor

Dr. Bao-Feng Feng

Third Advisor

Dr. Tim Huber

Abstract

In this thesis, we restrict our attention to nonlinear Duffing–van der Pol–type oscillator system by means of the First-integral method. This system has physical relevance as a model in certain flow-induced structural vibration problems, which includes the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. Firstly we apply the Division Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to explore a quasi-polynomial first integral to an equivalent autonomous system. Then through a certain parametric condition, we derive a more general first integral of the Duffing–van der Pol–type oscillator system.

Comments

Copyright 2011 Xiaochuan Hu. All Rights Reserved.

https://www.proquest.com/dissertations-theses/first-integral-method-duffing-van-der-pol-type/docview/896956370/se-2?accountid=7119

Granting Institution

University of Texas-Pan American