Complex Behavior in Leaky Faucet Experiment

Author(s)

Reynaldo Daniel Pinto

• Document type: Doctoral Thesis
• Press: São Paulo.
• Institution: Universidade de São Paulo (USP). Instituto de Física (IF/SBI)
• Defense date: 1999-03-19

Examining board members

Jose Carlos Sartorelli; Paulo Murilo Castro de Oliveira; Sérgio Machado Rezende; Silvio Roberto de Azevedo Salinas; Constantino Tsallis

• Advisor: Jose Carlos Sartorelli

Abstract

We assembled an experimental apparatus to study the dynamical complex behavior of water drop formation in a nipple faucet. We developed a closed hydrodynamic circuitry, and an automated acquisition data system, which also controls the faucet (a needle valve) opening. We have used as a control parameter the dripping rate set up by the faucet opening. For each dripping rate, the data are interdrop time series {Tn} between two successive drops. With the help of bifurcation diagrams, and reconstructed phase spaces in first return maps Tn+I x Tn, we were able to observe period doubling, Hopf bifurcation, interior and boundary crises, intermittent behaviors, and quasiperiodic movements. An anti-control of chaos was applied by perturbing a stable fixed point with pulses of compressed air on the nipple faucet. We also started the development of a technique to apply the control of chaos. The occurrence of saddle points was verified in some experimental attractors. By applying symbolic dynamics, we were able to observe homoclinic tangencies associated with the appearence of Hénon-like attractors and homoclinic bifurcations. By means of topological characterization, we established two routes to chaos related to homoclinic tangencies. We also observed, at high dripping rates, a sudden disappearance of a chaotic attractor due to a \"chaotic blue sky catastrophe\", just seen in a Van der Pol model used to simulate cardiac dynamics. (AU)