Interaction of two walkers: Perturbed vertical dynamics as a source of chaos

Walkers are dual objects comprising a bouncing droplet dynamically coupled to an underlying Faraday wave at the surface of a vibrated bath. In this paper, we study the wave-mediated interaction of two walkers launched at one another, both experimentally and theoretically. Different outcomes are observed in which either the walkers scatter or they bind to each other in orbits or promenade-like motions. The outcome is highly sensitive to initial conditions, which is a signature of chaos, though the time during which perturbations are amplified is finite. The vertical bouncing dynamics, periodic for a single walker, is also strongly perturbed during the interaction, owing to the superposition of the wave contributions of each droplet. Thanks to a model based on inelastic balls coupled to the Faraday waves, we show that this perturbed vertical dynamics is the source of horizontal chaos in such a system.