The Dripping Faucet as a Model Chaotic System

Description

Water drops falling from an orifice present a system which is both easily accessible to experiment and common in everyday life. As the flow rate is varied, many features of the phenomenology on nonlinear systems can be seen, including chaotic transitions, familiar and unfamiliar bifurcation sequences, hysterisis, and multiple basins of attraction. Observation of a physical system in a chaotic regime raises general questions concerning the modeling process. Given a stream of data from an experiment, how does one construct a representation of the deterministic aspects of the system? Elementary information theory provides a basis for quantifying the predictability of noisy dynamical systems. Examples are given from the experimental data of computations of the two dynamical invariants: a) the information stored in a system, and b) the entropy, or rate of loss of this information.