糖心TV

The dynamics of many complex systems are governed by inherently nonlinear processes determining both, their 鈥渕acroscopic鈥� dynamics as well as their 鈥渕icroscopic鈥� structural organization. This applies in particular to systems composed of individual, mutually interacting subsystems, which may either be discrete entities (e.g., neurons in the human brain or clusters thereof) or form a continuum (e.g., in spatially extended systems like the Earth鈥檚 atmosphere or ocean, which are commonly observed in some spatially discretized form only). In both cases, classical concepts of multivariate statistics are commonly not sufficient to empirically characterize the emerging spatio-temporal dynamical patterns and deduce information on the (not directly observable) spatial structure of the underlying physical processes. As an alternative, complex networks provide a versatile toolbox for inferring so-called 鈥渇unctional connectivity鈥� relationships from spatio-temporal data sets based on statistical associations and thus characterize spatial structures in a way that is commonly hidden to other long established analysis techniques.

This lecture series provides an introduction to the use of complex network methods for understanding the dynamics of complex systems based on multivariate as well as univariate time series. After a brief recap of the conceptual foundations of such approaches, I will focus on the following main topics:

Functional network analysis: basic ideas, climate networks, relationship with EOF analysis, functional connectivity based on non-conventional statistical association measures, spatial effects in climate networks, coupled climate networks, applications and open methodological challenges

Time series analysis by complex networks: categories of approaches, recurrence based methods (recurrence plots, recurrence quantification analysis, recurrence networks, bi- and multivariate generalizations, applications), visibility graphs and algorithmic variants thereof, transition matrices and their network interpretations (symbolic dynamics and order pattern based transition networks)

Flow networks: transition network representation of Lagrangian dynamics in (low-dimensional) dynamical systems and real-world flows