Coexisting Asymmetric and Symmetric Periodic Motions in the Mathieu-Duffing Oscillator

In this paper, periodic motions in the Mathieu-Duffing oscillator are analytically predicted through the harmonic balance method. The approximate, analytical solutions of periodic motions are achieved, and the corresponding stability analyses of the stable and unstable periodic solutions are completed. Numerical simulations are provided for a complete picture of coexisting periodic motions.