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DDC: 530 × Has files: Yes × Subject: climate ×

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Now showing 1 - 4 of 4
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    Local difference measures between complex networks for dynamical system model evaluation
    (San Francisco, CA : Public Library of Science (PLoS), 2015) Lange, S.; Donges, J.F.; Volkholz, J.; Kurths, J.
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    Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics
    (San Francisco, CA : Public Library of Science (PLoS), 2016) Tupikina, L.; Molkenthin, N.; López, C.; Hernández-García, E.; Marwan, N.; Kurths, J.
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    Networks from Flows - From Dynamics to Topology
    (London : Nature Publishing Group, 2014) Molkenthin, N.; Rehfeld, K.; Marwan, N.; Kurths, J.
    Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.
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    Recurrence flow measure of nonlinear dependence
    (Berlin ; Heidelberg : Springer, 2022) Braun, Tobias; Kraemer, K. Hauke; Marwan, Norbert
    Couplings in complex real-world systems are often nonlinear and scale dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence-based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. Using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence-based state space reconstruction algorithm.