Active Soft-Impact Oscillator: Dynamics of a Walking Droplet in a Non-Smooth Potential

TL;DR

This paper models a walking droplet as an active soft-impact oscillator within a non-smooth potential, revealing complex nonlinear behaviors and bifurcations, and providing insights into hydrodynamic quantum analogs.

Contribution

It introduces a novel active soft-impact oscillator model coupling non-smooth impacts with wave-particle dynamics, advancing understanding of impact-driven nonlinear phenomena.

Findings

Identification of impact and grazing-induced bifurcations

Discovery of impact-free and impact-mediated attractor switching

Demonstration of complex chaotic and periodic behaviors

Abstract

Walking droplets are millimetric fluid drops that propel themselves across a vibrated liquid bath through interaction with their self-generated waves. They constitute classical active wave-particle entities and exhibit a range of hydrodynamic quantum analogs. We investigate an \emph{active soft-impact oscillator} as a minimal model for a walking droplet moving within a piecewise-smooth external potential, analogous to classical mass-spring soft-impact oscillators and recently explored quantum soft-impact oscillators. Our active soft-impact oscillator model couples a non-smooth soft-impact force to the Lorenz-like dynamics arising from the wave-particle entity. Theoretical and numerical exploration of the full parameter space reveals a wide variety of nonlinear behaviors and bifurcations driven by impact and grazing events. These include grazing-induced and impact-induced transitions between periodic and chaotic motion, as well as grazing-mediated attractor switching and impact-free (invisible) attractor switching. The active soft-impact oscillator thus provides a versatile platform for probing nonlinear impact dynamics in active systems and exploring hydrodynamic quantum analogs in non-smooth potentials.