Noisy scattering dynamics in the randomly driven Hénon-Heiles oscillator

Noisy scattering dynamics in the randomly driven Hénon-Heiles oscillator is investigated when the energy is above the threshold to permit particles to escape from the scattering region. First, some basic simulation procedures are briefly introduced and the fractal exit basins appear to be robust when the bounded noisy excitation is imposed on the oscillator. Second, several key fractal characteristics of the sample basin boundaries, such as the delay-time function and the uncertainty dimension, are estimated from which this oscillator is found to be structurally unstable against the bounded noisy excitation. Moreover, the stable and unstable manifolds of some sample chaotic invariant sets are estimated and illustrated in a special two-dimensional Poincaré section. Lastly, several previous methods are developed to identify three arbitrarily chosen noisy scattering time series of the randomly driven Hénon-Heiles oscillator, from which the quasiperiodic-dominant and the chaotic-dominant dynamical behaviors are distinguished.