On resonant separatrix layers of a twin-well Duffing oscillator

Abstract

In this paper, resonant separatrix layers in the Duffing oscillator with a twin-well potential are investigated through the energy incremental spectrum, and the corresponding parameter maps are also obtained. For the ( $$2n-1{:}1$$ )-resonant layers outside the potential wells, the existence domain in parameter map becomes large with increasing excitation amplitude or frequency. For the (m : 1)-resonant layers inside the potential wells, the existence domain in the parameter map is closed because the maximum natural frequency in the potential well is finite. The Poincare mapping sections for appearance and disappearance of resonant layers are carried out. For a specific resonant layer, with increasing excitation frequency and amplitude, the saddle and centers of the resonant layer are not on the same resonant orbit, which should be further investigated.