This paper develops semi-analytical solutions of periodic motions of the van der Pol oscillator. The van der Pol system is discretized to form implicit mappings. Based on specific mapping structures, the semi-analytical solutions are obtained accurately, and the independent bifurcation branches of periodic motions are also presented for a better understanding of the nonlinear characteristics of the van der Pol oscillator. Stability and bifurcations are carried out though eigenvalue analysis. For comparison of analytical and numerical solutions, numerical simulation is completed and displacement and trajectories are presented.

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