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

First integrals for the Duffing-van der Pol type oscillator

Guangyue Gao, Zhaosheng Feng

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.

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Guangyue Gao
Department of Mathematics, University of Texas-Pan American
Edinburg, TX 78539, USA
email: gygao@broncs.utpa.edu
Zhaosheng Feng
Department of Mathematics, University of Texas-Pan American
Edinburg, TX 78539, USA
email: zsfeng@utpa.edu fax: 956-381-5091

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