Inferring Indirect Coupling by Means of Recurrences

The identification of the coupling direction from measured time series taking place in a group of interacting components is an important challenge for many experimental studies. We propose here a method to uncover the coupling configuration using recurrence properties. The approach hinges on a generalization of conditional probability of recurrence, which was originally introduced to detect and quantify even weak coupling directions between two interacting systems, to the case of multivariate time series where indirect interactions might be present. We test our method by an example of three coupled Lorenz systems. Our results confirm that the proposed method has much potential to identify indirect coupling, which is very relevant for experimental time series analysis.

[1]  M. Rosenblum,et al.  Detecting direction of coupling in interacting oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  A. Tsonis,et al.  Topology and predictability of El Niño and La Niña networks. , 2008, Physical review letters.

[3]  O. Sporns,et al.  Motifs in Brain Networks , 2004, PLoS biology.

[4]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

[5]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[6]  Jürgen Kurths,et al.  Distinguishing direct from indirect interactions in oscillatory networks with multiple time scales. , 2010, Physical review letters.

[7]  Changsong Zhou,et al.  Hierarchical organization unveiled by functional connectivity in complex brain networks. , 2006, Physical review letters.

[8]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[9]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[10]  R. Andrzejak,et al.  Detection of weak directional coupling: phase-dynamics approach versus state-space approach. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  S. Bressler,et al.  Granger Causality: Basic Theory and Application to Neuroscience , 2006, q-bio/0608035.

[12]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[13]  Norbert Marwan,et al.  The backbone of the climate network , 2009, 1002.2100.

[14]  H Kantz,et al.  Direction of coupling from phases of interacting oscillators: a permutation information approach. , 2008, Physical review letters.

[15]  Uri Alon,et al.  An Introduction to Systems Biology , 2006 .

[16]  M. Rosenblum,et al.  Identification of coupling direction: application to cardiorespiratory interaction. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[18]  M. Paluš,et al.  Directionality of coupling from bivariate time series: how to avoid false causalities and missed connections. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Klaus Lehnertz,et al.  Detecting directional coupling in the human epileptic brain: limitations and potential pitfalls. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  J. Kurths,et al.  Influence of paced maternal breathing on fetal–maternal heart rate coordination , 2009, Proceedings of the National Academy of Sciences.

[21]  Jonathan F. Donges,et al.  Comparing linear and nonlinear network construction methods , 2009 .

[22]  Jürgen Kurths,et al.  Influence of observational noise on the recurrence quantification analysis , 2002 .

[23]  M. Paluš,et al.  Inferring the directionality of coupling with conditional mutual information. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  P. Grassberger,et al.  Characterization of Strange Attractors , 1983 .

[25]  秦 浩起,et al.  Characterization of Strange Attractor (カオスとその周辺(基研長期研究会報告)) , 1987 .

[26]  R. Quiroga,et al.  Learning driver-response relationships from synchronization patterns. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  S. Frenzel,et al.  Partial mutual information for coupling analysis of multivariate time series. , 2007, Physical review letters.

[28]  Jürgen Kurths,et al.  Estimation of the direction of the coupling by conditional probabilities of recurrence. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Matthäus Staniek,et al.  Symbolic transfer entropy. , 2008, Physical review letters.

[30]  S. Havlin,et al.  Climate networks around the globe are significantly affected by El Niño. , 2008, Physical review letters.