Leaky Tap Behavior Described by a Simple Discrete Mapping

Abstract

The complex variety of phenomena associated with the dynamical behavior of a dripping faucet is reproduced with a simple map deduced from a one-dimensional analog mass-on-spring simulation, which has a dependence on a reduced number of parameters. It is analyzed how the dynamics of the real tap depends on the flow rate and on the geometrical parameters of the tip. Experimental bifurcation diagrams and attractors illustrate the adherence of the mapping to the real dynamics. The enormous simplifications in reducing the actual physical system to a simple oscillator mapping allows to us to investigate more deeply the parameter space and to understand the most important dynamical mechanisms of the leaky tap.