On the determination of the limit cycles using the harmonic balance method

Several methods have been developed to search for limit cycles or bifurcation curves of nonlinear differential equations. Recently, some non-perturbative methods have been proposed. However, the majority of these methods are based on the so-called harmonic balance method. In this paper, we will see how to use the harmonic balance method to obtain information of the number, period, and form of the limit cycles of certain nonlinear equations. The method also gives a sequence of algebraic approximations of the limit cycles. We will also compare our results with other non-perturbative methods. The results can be generalized to other nonlinear differential equations. (C) 2013 AIP Publishing LLC.