RESONANT-OVERLAP PHENOMENA IN STOCHASTIC LAYERS OF NON-LINEAR HAMILTONIAN SYSTEMS WITH PERIODICAL EXCITATIONS

Abstract

An accurate standard-map approach, instead of the approximate standard-map approach, is developed for the analytical prediction of the onset of a new resonant overlap forming a new resonant-separatrix web in the stochastic layer. This accurate approach applies to the twin-well Duffing oscillator for illustration of the resonant overlap phenomena in stochastic layers. The excitation strengths are obtained analytically for the onset of the specified resonant-separatrix webs in the stochastic layer. This accurate approach gives a very good prediction compared to numerical results for the lower order resonant overlap. When excitation strength is very weak, the accurate and approximate standard-map methods are in good agreement, and the accurate one is applicable to non-linear systems with strong excitations. However, the further improvement should be completed for a more accurate, analytical prediction of the onset of a new resonant overlap in stochastic layers of non-linear Hamiltonian systems with periodical excitations.