Analytical and numerical study of the unstable limit cycles of walking droplets

Abstract

Recent studies have shown that a vibrating fluid bath can support a bouncing droplet, generating a pilot wave which propels the droplet into horizontal motion. Walking droplets have been demonstrated not only to follow linear trajectories, but to exhibit a range of rich dynamical behavior, including tunneling, diffraction, and orbital quantization. Current theoretical models for the walking droplet system can be difficult to analyze. Here, by reducing the dimension of the bath, a simpler model has been derived and analyzed. We summarize this derivation, explore the stability of the system's dynamical states, and provide evidence of a previously unreported homoclinic bifurcation.