Heteroclinic behavior in a dripping faucet experiment

• Published in: Physics letters. A 2002-07, Vol.300 (2), p.192-198
• Main Authors: Reyes, M.B, Pinto, R.D, Tufaile, A, Sartorelli, J.C
• Format: Article
• Language: English
• Subjects: Chaos; Drops; Heteroclinic
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/S0375-9601(02)00821-6

Heteroclinic tangles are ubiquitous and responsible for a large number of complex behaviors, like catastrophic bifurcations. We have found evidences of the presence of a heteroclinic scenario in the dripping faucet experiment by applying topological analysis. We have measured the time ( T n ) between the nth and ( n+1)th drops, and we have reconstructed the phase space of the system by plotting T n+1  vs. T n . Two control parameters were used, the faucet opening and the inclination ( θ) of the faucet measured from vertical position. We have already shown, for θ=0 (vertical) by varying the faucet opening, a boundary crisis known as chaotic blue sky catastrophe in which there is a sudden change of the attractive basins. For values of θ≠0° the system symmetry is broken and we have observed, even for small angles ( θ∼5°), strong changes in the attractors topology when compared with those obtained with the nozzle in the vertical position. Instead of the catastrophe, a smooth transition from a chaotic attractor to another one takes place, and it is possible to observe the attraction basins merged. We also have shown evidences of connections between the manifolds of two saddle points, resulting in a heteroclinic scenario.