Active Soft-Impact Oscillator: Dynamics of a Walking Droplet in a Non-Smooth Potential
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arXiv
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| Format: | Preprint |
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2026
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| author | Mukherjee, Titir Valani, Rahil N Banerjee, Soumitro |
| author_facet | Mukherjee, Titir Valani, Rahil N Banerjee, Soumitro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05913 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Active Soft-Impact Oscillator: Dynamics of a Walking Droplet in a Non-Smooth Potential Mukherjee, Titir Valani, Rahil N Banerjee, Soumitro Chaotic Dynamics Fluid Dynamics 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. |
| title | Active Soft-Impact Oscillator: Dynamics of a Walking Droplet in a Non-Smooth Potential |
| topic | Chaotic Dynamics Fluid Dynamics |
| url | https://arxiv.org/abs/2602.05913 |