On resonant separatrix bands of a Duffing oscillator with a twin-well potential

The chaotic motions in the resonant bands of the Duffing oscillator with a twin-well potential are investigated numerically in this paper. The resonant bands are illustrated through the Poincare mapping sections, and the deviation of saddle points of the resonant separatrix band is observed for the onset of the resonant band. The onset and disappearance of a specific resonant band are investigated through the incremental energy spectrum method. The intermittency either between the two closest resonant bands or between the resonant band and the stochastic layer is observed. Just before the resonant band is destroyed, it is very clearly observed that the self-similarity is induced by the sub-resonance. The three phenomena exist in resonant bands of other nonlinear Hamiltonian systems.