scholarly journals Formulas for the Amplitude of the van der Pol Limit Cycle through the Homotopy Analysis Method

2009 ◽  
Vol 2009 ◽  
pp. 1-7 ◽  
Author(s):  
J. L. López ◽  
S. Abbasbandy ◽  
R. López-Ruiz
Keyword(s):  
Limit Cycle ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Van Der Pol ◽  
Homotopy Analysis

scholarly journals Application of Extended Homotopy Analysis Method to the Two-Degree-of-Freedom Coupled van der Pol-Duffing Oscillator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Y. H. Qian ◽  
S. M. Chen ◽  
L. Shen
Keyword(s):  
Homotopy Analysis Method ◽  
Duffing Oscillator ◽  
Approximate Solutions ◽  
Analytical Approximation ◽  
Degree Of Freedom ◽  
Analysis Method ◽  
Van Der Pol ◽  
Different Types ◽  
Homotopy Analysis ◽  
Two Degree Of Freedom

The extended homotopy analysis method (EHAM) is presented to establish the analytical approximate solutions for two-degree-of-freedom (2-DOF) coupled van der Pol-Duffing oscillator. Meanwhile, the comparisons between the results of the EHAM and standard Runge-Kutta numerical method are also presented. The results demonstrate that the analytical approximate solutions of the EHAM agree well with the numerical integration solutions. For EHAM as an analytical approximation method, we are not sure whether it can apply to all of the nonlinear systems; we can only verify its effectiveness through specific cases. As a result of the existence of nonlinear terms, we must study different types of systems, no matter from the complication of calculation and physical significance.

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