CHAOTIC MOTION IN THE GENERIC SEPARATRIX BAND OF A MATHIEU–DUFFING OSCILLATOR WITH A TWIN-WELL POTENTIAL

The resonant conditions for the Mathieu–Duffing oscillator are determined, and the resonant orders for the inside and outside of the generic separatrix are (M:1) and (2 M:1) respectively. The excitation strength for the onset of a specific resonance in the generic separatrix band is predicted analytically and numerically through the incremental energy approach and the energy spectrum methods. For comparison of the separatrix splitting theory, the widths of the generic separatrix band are computed through the maximum and minimum energies. The bandwidth is not linear to the excitation strength, and it is strongly dependent on the resonance. The results can be applied to the post-buckled structures under parametric excitation forces. However, the chaotic motion in the resonant separatrix band needs to be investigated for a better understanding of chaotic motion in the Mathieu–Duffing oscillator.