We propose a simple model for the chaotic dripping of a faucet in terms of a return map constructed by
analyzing the stability of a pendant drop. The return
map couples two classical normal forms, an Andronov
saddle-node bifurcation, and a Shilnikov homoclinic bifurcation. The former corresponds to the initiation of the
instability when the drop volume exceed a critical value
set by the balance between surface tension and gravity,
while the latter models the global reinjection associated
with pinch-off that eventually return the drop to a state
close to its original unstable configuration. The results
obtained using the return map are consistent with those
of numerical simulations of the governing PDEs and prior
experiments, and show periodic and quasi-periodic dripping at low and high flow rates, and chaotic behavior at
intermediate flow rates.