Controlling unpredictability in the randomly driven H\'enon-Heiles system

TL;DR

This paper explores how external perturbations like dissipation and random-phase forcing influence unpredictability in the chaotic scattering of the Hénon-Heiles system, identifying conditions that lead to Wada basin boundaries and increased predictability.

Contribution

It demonstrates how dissipation can reduce unpredictability by reconfiguring basin boundaries and identifies parameter regimes where Wada basins occur in the system.

Findings

Dissipation can make the system more predictable by reassembling basin boundaries.

External forcing with a random phase increases unpredictability and Wada basin properties.

Specific relationships between damping, forcing amplitude, and energy determine the basin boundary properties.

Abstract

Noisy scattering dynamics in the randomly driven H\'enon-Heiles system is investigated in the range of initial energies where the motion is unbounded. In this paper we study, with the help of the exit basins and the escape time distributions, how an external perturbation, be it dissipation or periodic forcing with a random phase, can enhance or mitigate the unpredictability of a system that exhibit chaotic scattering. In fact, if basin boundaries have the Wada property, predictability becomes very complicated, since the basin boundaries start to intermingle, what means that there are points of different basins close to each other. The main responsible of this unpredictability is the external forcing with random phase, while the dissipation can recompose the basin boundaries and turn the system more predictable. Therefore, we do the necessary simulations to find out the values of dissipation and external forcing for which the exit basins present the Wada property. Through these numerical simulations, we show that the presence of the Wada basins have a specific relation with the damping, the forcing amplitude and the energy value. Our approach consists on investigating the dynamics of the system in order to gain knowledge able to control the unpredictability due to the Wada basins.