Theses and Dissertations - UTB/UTPA

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Zhaosheng Feng

Second Advisor

Dr. Bao-Feng Feng

Third Advisor

Dr. Tim Huber


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.


Copyright 2011 Xiaochuan Hu. All Rights Reserved.

Granting Institution

University of Texas-Pan American

Included in

Mathematics Commons