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Grant support

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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Seoane, JmCorresponding AuthorMarino, IpAuthorSanjuan, MafAuthor

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September 27, 2022
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Basin boundary metamorphoses and phase control

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

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

Affiliations

Univ Rey Juan Carlos, Dept Fis, Madrid 28933, Spain - Author

Abstract

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.

Keywords

Chaotic scatteringPerturbations

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Epl due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2010, it was in position 16/80, thus managing to position itself as a Q1 (Primer Cuartil), in the category Physics, Multidisciplinary.

Independientemente del impacto esperado determinado por el canal de difusión, es importante destacar el impacto real observado de la propia aportación.

Según las diferentes agencias de indexación, el número de citas acumuladas por esta publicación hasta la fecha 2025-08-13:

  • WoS: 3
  • Scopus: 3

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-08-13:

  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 3 (PlumX).

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (Seoane Sepúlveda, Jesús Miguel) and Last Author (Fernández Sanjuán, Miguel Ángel).

the author responsible for correspondence tasks has been Seoane Sepúlveda, Jesús Miguel.