Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems

Abstract

We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.

10 pages, 8 figures

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• Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package
• Extreme events in dynamical systems and random walkers: A review
• Measure for degree heterogeneity in complex networks and its application to recurrence network analysis
• Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data
• Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics
• Uniform framework for the recurrence-network analysis of chaotic time series
• Early warning signals for critical transitions in complex systems
• Disentangling synchrony from serial dependency in paired event time series
• Identifying edges that facilitate the generation of extreme events in networked dynamical systems
• Can recurrence networks show small world property?
• Study of Interaction and Complete Merging of Binary Cyclones Using Complex Networks
• Quantifying information loss on chaotic attractors through recurrence networks
• Synchronization of complex spatio-temporal dynamics with lasers