Torus breakdown and noise-induced dynamics in the randomly driven Morse oscillator

Strictly, the KAM torus no longer exists for a randomly driven Hamiltonian system. We firstly investigate the process of torus breakdown in the randomly driven Morse oscillator by transforming the original system into another one in action-angle variables and introducing the specific Poincaré map by Makarov et al. Though the strength of random perturbations is large, some thick closed-like curves can still appear. To characterize these noisy dynamics, the pseudo-periodic surrogate approach, along with the algorithm on the mean divergence, is applied to evaluate the correlation dimensions of the original data and their corresponding surrogates. Two kinds of noisy dynamics are picked out from the randomly driven Morse oscillator.