title: Distinguishing noise from chaos: objective versus subjective criteria using horizontal visibility graph.
abstract: 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.
authors.affiliation: Departamento de Engenharia de Produção, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil; Departament de Física Fonamental, Universitat de Barcelona, Barcelona, Spain.
authors.forename: Martín Gómez
authors.initials: MG
authors.lastname: Ravetti
authors.affiliation: Laboratório de Computação Científica e Análise Numérica (LaCCAN), Universidade Federal de Alagoas, Maceió, Alagoas, Brazil.
authors.forename: Laura C
authors.initials: LC
authors.lastname: Carpi
authors.affiliation: Departamento de Engenharia de Produção, Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil; Instituto Politécnico. Centro Universitário UNA, Belo Horizonte, Minas Gerais, Brazil.
authors.forename: Bruna Amin
authors.initials: BA
authors.lastname: Gonçalves
authors.affiliation: Laboratório de Computação Científica e Análise Numérica (LaCCAN), Universidade Federal de Alagoas, Maceió, Alagoas, Brazil.
authors.forename: Alejandro C
authors.initials: AC
authors.lastname: Frery
authors.affiliation: Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas - Brazil; Instituto Tecnológico de Buenos Aires (ITBA), Ciudad Autónoma de Buenos Aires, Argentina.
authors.forename: Osvaldo A
authors.initials: OA
authors.lastname: Rosso
mesh_terms: D000465:Algorithms; D019295:Computational Biology; D017711:Nonlinear Dynamics; D013269:Stochastic Processes