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We would like to thank J. C. VALLEJO for the fruitful discussions we had during the development of this work. The basins of attraction (fig. 1 and fig. 5) have been made using the software DYNAMICS [22]. This work was supported by the Spanish Ministry of Education and Science under project No. FIS2006-08525 and by the Spanish Ministry of Science and Innovation under project No. FIS2009-09898.

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Basin boundary metamorphoses and phase control

Publicado en:Epl. 90 (3): 30002- - 2010-05-01 90(3), DOI: 10.1209/0295-5075/90/30002

Autores: Seoane, J M; Zambrano, S; Marino, I P; Sanjuan, M A F

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Resumen

Basin boundary metamorphoses are characteristic in some kinds of chaotic dynamical systems. They take place when one parameter of the system is varied and it passes through a certain critical value. In this paper we show that a parametric harmonic perturbation can produce basin boundary metamorphoses in periodically driven chaotic dynamical systems even when its amplitude is smaller than the amplitude of the main driving. The physical context of this work is related with the phenomenon of trajectories escaping from a potential well, which is illustrated by using as prototype model the Helmholtz oscillator. One of the main contributions of our research is to analyze the role of the phase difference between the parametric harmonic perturbation and the main driving in the appearance of a basin boundary metamorphosis. We also analyze the variation of the size of the basins and the fractal dimension of the corresponding boundaries when this phenomenon occurs. Finally, Melnikov analysis of this phenomenon is carried out. We expect that this work can be useful for a better understanding of basin boundary metamorphoses phenomena.

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