Crises and chaotic scattering in hydrodynamic pilot-wave experiments

TL;DR

This paper explores how hydrodynamic pilot-wave experiments can serve as a bridge to understand the transition from low- to high-dimensional chaos, revealing complex scattering and crisis bifurcations.

Contribution

It demonstrates experimentally how chaotic attractors form and merge in pilot-wave systems, linking low- and high-dimensional chaos in a systematic way.

Findings

Formation of low-dimensional chaotic attractors upon destabilization.

Transition to high-dimensional chaos via merging of chaotic regions.

Post-crisis dynamics characterized by scattering from nonattracting chaotic sets.

Abstract

Theoretical foundations of chaos have have been predominantly laid out for finite-dimensional dynamical systems, such as the three-body problem in classical mechanics and the Lorenz model in dissipative systems. In contrast, many real-world chaotic phenomena, e.g. weather, arise in systems with many (formally infinite) degrees of freedom, which limits direct quantitative analysis of such systems using chaos theory. In the present work, we demonstrate that the hydrodynamic pilot-wave systems offer a bridge between low- and high-dimensional chaotic phenomena by allowing for a systematic study of how the former connects to the latter. Specifically, we present experimental results which show the formation of low-dimensional chaotic attractors upon destabilization of regular dynamics and a final transition to high-dimensional chaos via the merging of distinct chaotic regions through a crisis bifurcation. Moreover, we show that the post-crisis dynamics of the system can be rationalized as consecutive scatterings from the nonattracting chaotic sets with lifetimes following exponential distributions.