Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph.
A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque et al., Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa et al., Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study t...
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| Format: | Article |
| Language: | English |
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Public Library of Science (PLoS)
2014-01-01
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| Series: | PLoS ONE |
| Online Access: | https://doi.org/10.1371/journal.pone.0108004 |
| _version_ | 1797260315116699648 |
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| author | Martín Gómez Ravetti Laura C Carpi Bruna Amin Gonçalves Alejandro C Frery Osvaldo A Rosso |
| author_facet | Martín Gómez Ravetti Laura C Carpi Bruna Amin Gonçalves Alejandro C Frery Osvaldo A Rosso |
| author_sort | Martín Gómez Ravetti |
| collection | DOAJ |
| description | A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque et al., Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa et al., Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form [Formula: see text], in which [Formula: see text] is the node degree and [Formula: see text] is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to [Formula: see text] chaotic maps, 2 chaotic flows and [Formula: see text] different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study. |
| first_indexed | 2024-04-24T23:23:22Z |
| format | Article |
| id | doaj.art-f94bdb6f88ae47ffbcfe9df81f5a4115 |
| institution | Directory Open Access Journal |
| issn | 1932-6203 |
| language | English |
| last_indexed | 2024-04-24T23:23:22Z |
| publishDate | 2014-01-01 |
| publisher | Public Library of Science (PLoS) |
| record_format | Article |
| series | PLoS ONE |
| spelling | doaj.art-f94bdb6f88ae47ffbcfe9df81f5a41152024-03-16T05:33:42ZengPublic Library of Science (PLoS)PLoS ONE1932-62032014-01-0199e10800410.1371/journal.pone.0108004Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph.Martín Gómez RavettiLaura C CarpiBruna Amin GonçalvesAlejandro C FreryOsvaldo A RossoA recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque et al., Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa et al., Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form [Formula: see text], in which [Formula: see text] is the node degree and [Formula: see text] is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to [Formula: see text] chaotic maps, 2 chaotic flows and [Formula: see text] different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study.https://doi.org/10.1371/journal.pone.0108004 |
| spellingShingle | Martín Gómez Ravetti Laura C Carpi Bruna Amin Gonçalves Alejandro C Frery Osvaldo A Rosso Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph. PLoS ONE |
| title | Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph. |
| title_full | Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph. |
| title_fullStr | Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph. |
| title_full_unstemmed | Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph. |
| title_short | Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph. |
| title_sort | distinguishing noise from chaos objective versus subjective criteria using horizontal visibility graph |
| url | https://doi.org/10.1371/journal.pone.0108004 |
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