Eighth Mississippi State - UAB Conference on Differential Equations and
Computational Simulations.
Electron. J. Diff. Eqns., Conference 19 (2010), pp. 123-133.

Title: First integrals for the Duffing-van der Pol type oscillator

Authors: Guangyue Gao (Univ. of Texas-Pan American, Edinburg, TX, USA)
         Zhaosheng Feng (Univ. of Texas-Pan American, Edinburg, TX, USA)
 
Abstract: 
 In this article, under certain parametric conditions,
 we study the first integrals of the Duffing-van der Pol-type
 oscillator equations which include the van der Pol and the
 Duffing oscillator systems, as particular cases.
 After making a series of variable transformations and applying
 the Preller-Singer method, we find the first integrals of the
 simplified equations without complicated calculations.
 Through the inverse transformations we obtain the first
 integrals of the original equations. Some statements in the
 literature are indicated and clarified.

Published September 25, 2010.
Math Subject Classifications: 34A25, 34L30.
Key Words: First integral; Duffing oscillator;  van der Pol oscillator; 
           Preller-Singer method; parametric solution.