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Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation
Y.M. Chen,J.K. Liu *
Department of Mechanics, Sun Yat-sen University, Guangzhou 510275, China
*Correspondence author
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Funding: 国家自然科学基金,教育部博士点基金,广东省自然科学基金,广东省自然科学基金（No.10772202，20050558032，07003680, 05003295）
Opened online: 5 January 2009
Accepted by: none
Citation: Y.M. Chen,J.K. Liu.Uniformly valid frequency solution of the limit cycle of the Duffing-van der Pol equation[OL]. [ 5 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27342
 
 
The limit cycle of the Duffing-van der Pol equation is studied. First, an equivalent equation is obtained by considering the product of the frequency of the limit cycle and the coefficient as an independent parameter . Then, the frequency is obtained as a function of and by solving the equivalent equation via the homotopy analysis method. This function provides us with an algebraic equation in . Solving this algebraic equation, an analytical approximation for the frequency is obtained. Numerical examples show that the attained approximation is very accurate and more importantly uniformly valid for all positive values of .
Keywords:Duffing-van der Pol equation;limit cycle;uniformly valid
 
 
 

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