Coupled Networks, Patterns and Complexity - Abstract
Palus, Milan
Networks of interacting dynamical systems have recently been attracting attention of both theorists and experimentalists as they represent a new paradigm for understanding emergent phenomena in complex systems and tools for novel analyses of multivariate and spatio-temporal data [1]. A multivariate time series is converted into a (weighted) graph by quantification of pair-wise dependence between time series representing dynamical evolution of individual systems nodes of the network. Then the graph theory is used to identify important features of the studied coupled systems such as scale-free or small-world topology, highly connected hubs and modularity, and helps to understand information or mass transfers among the subsystems. However, the existence of a link, its weight and/or direction is inferred from a dependence measure estimated from the available time series. Various sources of bias and confounding effects can distort the results of such inferences. In particular, character of temporal dynamics of a node (e.g. serial correlations/autocorrelation, or longterm memory) can influence dependence measures (e.g., Pearsons correlations, mutual information) with other nodes [2]. In studies of climate networks, using gridded surface air temperature anomalies (i.e., temperature series in which the average annual cycle is removed), several authors [3,4] identified the tropical Pacific areas as the most connected elements of the climate network and looked for interpretations in teleconnections of the El Nino phenomenon [3]. Using entropy rates of stochastic dynamical systems, however, we show that dynamics of the temperature anomalies from these areas are characterized by the lowest entropy rates, i.e., they have the most regular dynamics and the strongest dynamical memory. This property biases upward all measures of dependence of these areas with the rest of the world. Therefore Palus et al. [5] propose properly weighted connectivity measures combined with the surrogate data testing [2] accounting for such bias. The correction leads to dramatic changes in the topology of climate networks, in particular, the role of the North Atlantic Oscillation in the connectivity of global climate networks is sharply increased at the cost of the role of the El Nino Southern Oscillation. In further development we study information-theoretic approaches to quantify similarity of dynamics instead of quantifying similarity of static probability distributions. In examples of climate networks we show how highly connected hubs are identified, related to the leading modes of atmospheric variability. newline Acknowledgement: newline This study is supported by the Czech Science Foundation, Project No. P103/11/J068. newline References: newline [1] S Boccaletti, V Latora, Y Moreno, M Chavez, and D U Hwang, Complex networks: Structure and dynamics, Phys. Rep., 424(4-5), 175?308 (2006) newline [2] M Palus, From Nonlinearity to Causality: Statistical testing and inference of physical mechanisms underlying complex dynamics, Contemp. Phys., 48(6), 307?348 (2007) newline [3] A A Tsonis and K L Swanson, Topology a predictability of El Nino and La Nina networks, Phys. Rev. Lett., 100, 228502 (2008) newline [4] J F Donges, Y Zou, N Marwan, and J Kurths, The backbone of the climate network, Europhys. Lett., 87(4), 48007 (2009) newline 5] M Palus, D Hartman, J Hlinka, and M Vejmelka, Discerning connectivity from dynamics in climate networks, Nonlin. Processes Geophys., 18, 751-763 (2011)