Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis

A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system and the links account for their interactions, which arise due to a variety of mechanisms and which are often unknown. A popular method for inferring...

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Published in:	Scientific reports Vol. 5; no. 1; p. 10829
Main Authors:	Tirabassi, Giulio, Sevilla-Escoboza, Ricardo, Buldú, Javier M., Masoller, Cristina
Format:	Journal Article Publication
Language:	English
Published:	London Nature Publishing Group UK 04.06.2015 Nature Publishing Group Macmillan Publishers
Subjects:	639/766/259 639/766/530/2801 climate networks complex networks Complex networks and dynamic systems Connectivity fluctuations Física Humanities and Social Sciences information theory and computation Informàtica Mathematical models Methods Models matemàtics multidisciplinary Nodes Oscillators Science Similarity measures Sistemes complexos Statistics synchronization Time series Àrees temàtiques de la UPC
ISSN:	2045-2322, 2045-2322
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Abstract	A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system and the links account for their interactions, which arise due to a variety of mechanisms and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rössler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones.
AbstractList	A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rössler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones.A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rössler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones. A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rössler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones. A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rossler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones. Peer Reviewed
ArticleNumber	10829
Author	Sevilla-Escoboza, Ricardo Buldú, Javier M. Tirabassi, Giulio Masoller, Cristina
Author_xml	– sequence: 1 givenname: Giulio surname: Tirabassi fullname: Tirabassi, Giulio organization: Departament de Fisica i Enginyeria Nuclear, Universitat Politécnica de Catalunya – sequence: 2 givenname: Ricardo surname: Sevilla-Escoboza fullname: Sevilla-Escoboza, Ricardo organization: Center for Biomedical Technology, Technical University of Madrid – sequence: 3 givenname: Javier M. surname: Buldú fullname: Buldú, Javier M. organization: Centro Universitario de los Lagos, Universidad de Guadalajara, Complex Systems Group, Universidad Rey Juan Carlos – sequence: 4 givenname: Cristina surname: Masoller fullname: Masoller, Cristina organization: Departament de Fisica i Enginyeria Nuclear, Universitat Politécnica de Catalunya
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SubjectTerms	639/766/259 639/766/530/2801 climate networks complex networks Complex networks and dynamic systems Connectivity fluctuations Física Humanities and Social Sciences information theory and computation Informàtica Mathematical models Methods Models matemàtics multidisciplinary Nodes Oscillators Science Similarity measures Sistemes complexos Statistics synchronization Time series Àrees temàtiques de la UPC
Title	Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis
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