The charged bouncing ball: An experimental model for period-doubling bifurcation

Abstract

This paper presents an experimental and theoretical study of the dynamics of a conducting ball in a poorly conducting liquid subjected to an electric field. When the applied voltage is constant the ball bounces regularly on the lower electrode. If an AC voltage is superimposed, with a period equal to the unperturbed time between impacts, the ball undergoes a period-doubling bifurcation when increasing the amplitude of the AC signal. The non-linear map which describes the dynamics of the ball is closely related to the standard map and to the classical problem of a bouncing ball on a moving table.