Chaotic motion in the resonant separatrix bands of a Mathieu–Duffing oscillator with a twin-well potential

The (M:1)-resonant bands in the left and right potential wells are skew-symmetric, and the (2M:1)-resonant bands of the large orbit motion are symmetric. The analytical conditions for the onset and destruction of a resonant band are developed through the incremental energy approach. The numerical predictions of such onset and destruction are also completed by the energy increment spectrum method. The sub-resonance interaction occurs for strong excitations, which needs to be further investigated. These results are applicable to the small- and large-orbit motions of post-buckled structure under a parametric excitation.