Return map for the chaotic dripping faucet

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 an Andronov saddle-node bifurcation corresponding to the instability of the drop whose volume exceed a critical value, and a Shilni kov homoclinic bifurcation induced by the presence of a weakly damped oscil latory mode. We show that the predictions of the return map are qualitative ly consistent with the experimental results. We compare these results with those of a delay map constructed from the solution of an asymptotic lubrica tion model for the evolution of the dripping faucet.