An Accurate Standard Mapping Method for Stochastic Layers in Nonlinear Hamiltonian Systems

Abstract

An accurate standard mapping approach based on the exact period and energy approximations is developed for prediction of the onset of a new resonance in the stochastic layer. This accurate approach applies to the twin-well Duffing oscillator and a parametrically excited pendulum for prediction of the resonant characteristics in stochastic layers as sample problems. From examples, this accurate approach gives a better prediction than the approximate method, compared to numerical results.