From Memory-Driven Chaos to Markovian Dynamics in One-Dimensional Pilot-Wave Hydrodynamics

We investigate the dynamics of a one-dimensional memory-driven bouncing droplet confined by a symmetric

single-well potential in the high-memory regime, where the motion of a free droplet is chaotic and unpredictable.

Employing the one-dimensional stroboscopic model, we demonstrate that when the confining potential is sufficiently

strong, the droplet’s dynamics transition from chaotic and memory-driven to fully predictable and effectively Markovian.

In this limit, the system can be described by a nonautonomous ordinary differential equation, significantly reducing

its complexity. Our results underscore how external constraints can suppress the chaotic effects of temporal memory,

providing new insights into the emergence of Markovian, predictable behavior from chaotic systems governed by

history-dependent dynamics.