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Limit Cycles of Nonlinear Oscillator Equations with Absolute Value by Means of the Homotopy Analysis Method

Abstract An analytic approach based on the homotopy analysis method is proposed to obtain the limit cycles of highly nonlinear oscillating equations with absolute value terms. The non-smoothness of the absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach. It has general meanings and thus can be used to solve many other highly nonlinear oscillating systems with this kind of non-smoothness.