title: Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis.
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.
authors.affiliation: Departament de Fisica i Enginyeria Nuclear, Universitat Politécnica de Catalunya, 08222 Terrassa, Barcelona, Spain.
authors.forename: Giulio
authors.initials: G
authors.lastname: Tirabassi
authors.affiliation: Center for Biomedical Technology, Technical University of Madrid, Pozuelo de Alarcón, 28223 Madrid, Spain.
authors.forename: Ricardo
authors.initials: R
authors.lastname: Sevilla-Escoboza
authors.affiliation: 1] Centro Universitario de los Lagos, Universidad de Guadalajara, Lagos de Moreno, Jalisco 47460, Mexico [2] Complex Systems Group, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain.
authors.forename: Javier M
authors.initials: JM
authors.lastname: Buldú
authors.affiliation: Departament de Fisica i Enginyeria Nuclear, Universitat Politécnica de Catalunya, 08222 Terrassa, Barcelona, Spain.
authors.forename: Cristina
authors.initials: C
authors.lastname: Masoller