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>Methods to study complex systems

related to PIK research on Time Series Analysis and Complex Networks

Recurrence plots

Recurrence Plot

Recurrence plots (RPs) provide an alternative way to study various aspects of complex systems, such regime transitions, classification, detection of time-scales, synchronisation, and coupling detection (RP bibliography). Main contributions have been in bivariate extensions (cross RPs) and coupling analysis, new measures of complexity, significance assessments of the RP based results, spatial extensions, parameter selection, RPs for irregularly sampled data and for extreme events data, or complex network based quantification.

  • N. Marwan, M. C. Romano, M. Thiel and J. Kurths: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5–6), 237–329 (2007). DOI:10.1016/j.physrep.2006.11.001
  • N. Marwan, J. F. Donges, Y. Zou, R. V. Donner and J. Kurths: Complex network approach for recurrence analysis of time series, Physics Letters A, 373(46), 4246–4254 (2009). DOI:10.1016/j.physleta.2009.09.042
  • N. Marwan: How to avoid potential pitfalls in recurrence plot based data analysis, International Journal of Bifurcation and Chaos, 21(4), 1003–1017 (2011). DOI:10.1142/S0218127411029008
  • N. Marwan, S. Schinkel and J. Kurths: Recurrence plots 25 years later – Gaining confidence in dynamical transitions, Europhysics Letters, 101, 20007 (2013). DOI:10.1209/0295-5075/101/20007
  • T. Braun, V. R. Unni, R. I. Sujith, J. Kurths and N. Marwan: Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure, Nonlinear Dynamics, 104, 3955–3973 (2021). DOI:10.1007/s11071-021-06457-5
  • N. Marwan: Challenges and perspectives in recurrence analyses of event time series, Frontiers in Applied Mathematics and Statistics, 9, 1129105 (2023). DOI:10.3389/fams.2023.1129105

Complex networks

Complex networks provide a powerful approach for analyzing extended and spatio-temporal systems, such as the climate by climate networks. We introduced the concept of event synchronisation into climate network analysis to enabling targeted studies of extreme events. Moreover, they offer an alternative way for a recurrence based time-series analysis by recurrence networks.

  • N. Malik, N. Marwan and J. Kurths: Spatial structures and directionalities in Monsoonal precipitation over South Asia, Nonlinear Processes in Geophysics, 17(5), 371–381 (2010). DOI:10.5194/npg-17-371-2010
  • N. Boers, B. Bookhagen, N. Marwan, J. Kurths and J. Marengo: Complex networks identify spatial patterns of extreme rainfall events of the South American Monsoon System, Geophysical Research Letters, 40(16), 4386–4392 (2013). DOI:10.1002/grl.50681
  • K. Rehfeld, N. Marwan, S. F. M. Breitenbach and J. Kurths: Late Holocene Asian summer monsoon dynamics from small but complex networks of paleoclimate data, Climate Dynamics, 41(1), 3–19 (2013). DOI:10.1007/s00382-012-1448-3
  • N. Marwan, S. Foerster and J. Kurths: Analysing spatially extended high-dimensional dynamics by recurrence plots, Physics Letters A, 379(10–11), 894–900 (2015). DOI:10.1016/j.physleta.2015.01.013
  • Y. Zou, R. V. Donner, N. Marwan, J. F. Donges and J. Kurths: Complex network approaches to nonlinear time series analysis, Physics Reports, 787, 1–97 (2019). DOI:10.1016/j.physrep.2018.10.005

Special time-series analysis methods for special problems

Absolute Age

Special problems require especially adopted methods of time-series analysis. For example, proxy records in Earth sciences are often irregularly sampled and come with uncertainties in the dating points. Approaches for considering such dating uncertainties in the subsequent analysis and methods for correlation analysis of irregularly sampled time series have been developed. Such approaches can be helpful for the reconstruction of palaeoclimate complex networks.

  • K. Rehfeld, N. Marwan, J. Heitzig and J. Kurths: Comparison of correlation analysis techniques for irregularly sampled time series, Nonlinear Processes in Geophysics, 18(3), 389–404 (2011). DOI:10.5194/npg-18-389-2011
  • S. F. M. Breitenbach, K. Rehfeld, B. Goswami, J. U. L. Baldini, H. E. Ridley, D. Kennett, K. Prufer, V. V. Aquino, Y. Asmerom, V. J. Polyak, H. Cheng, J. Kurths and N. Marwan: COnstructing Proxy-Record Age models (COPRA), Climate of the Past, 8, 1765–1779 (2012). DOI:10.5194/cp-8-1765-2012
  • D. Eroglu, F. H. McRobie, I. Ozken, T. Stemler, K.-H. Wyrwoll, S. F. M. Breitenbach, N. Marwan and J. Kurths: See-saw relationship of the Holocene East Asian-Australian summer monsoon, Nature Communications, 7, 12929 (2016). DOI:10.1038/ncomms12929
  • B. Goswami, N. Boers, A. Rheinwalt, N. Marwan, J. Heitzig, S. F. M. Breitenbach and J. Kurths: Abrupt transitions in time series with uncertainties, Nature Communications, 9, 48 (2018). DOI:10.1038/s41467-017-02456-6
  • I. Ozken, D. Eroglu, S. F. M. Breitenbach, N. Marwan, L. Tan, U. Tirnakli and J. Kurths: Recurrence plot analysis of irregularly sampled data, Physical Review E, 98, 052215 (2018). DOI:10.1103/PhysRevE.98.052215
  • N. Marwan and T. Braun: Power spectral estimate for discrete data, Chaos, 33(5), 053118 (2023). DOI:10.1063/5.0143224

>Complexity in applications

Climate and palaeoclimate

We use advanced data analysis methods, e.g., complex networks, to study spatio-temporal climate systems. One key product is the PIKART catalogue, the world-leading catalogue of atmospheric rivers. The study of palaeoclimate from proxy records is helpful for a better understanding of the climate system. Information based on lake sediments or speleothemes can be used to study complex interrelationships or past climate transitions. We are also participating in the coordinated scientific research in the Blessberg Cave, Thuringia.

Cover Science 2012
  • J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber and J. Kurths: Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution, Proceedings of the National Academy of Sciences, 108(51), 20422–20427 (2011). DOI:10.1073/pnas.1117052108
  • D. J. Kennett, S. F. M. Breitenbach, V. V. Aquino, Y. Asmerom, J. Awe, J. U. L. Baldini, P. Bartlein, B. J. Culleton, C. Ebert, C. Jazwa, M. J. Macri, N. Marwan, V. Polyak, K. M. Prufer, H. E. Ridley, H. Sodemann, B. Winterhalder and G. H. Haug: Development and Disintegration of Maya Political Systems in Response to Climate Change, Science, 338(6108), 788–791 (2012). DOI:10.1126/science.1226299
  • N. Boers, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Kurths and J. A. Marengo: Prediction of extreme floods in the eastern Central Andes based on a complex networks approach, Nature Communications, 5, 5199 (2014). DOI:10.1038/ncomms6199
  • A. Agarwal, L. Caesar, N. Marwan, R. Maheswaran, B. Merz and J. Kurths: Network-based identification and characterization of teleconnections on different scales, Scientific Reports, 9, 8808 (2019). DOI:10.1038/s41598-019-45423-5
  • M. Singh, R. Krishnan, B. Goswami, A. D. Choudhury, P. Swapna, R. Vellore, A. G. Prajeesh, N. Sandeep, C. Venkataraman, R. V. Donner, N. Marwan and J. Kurths: Fingerprint of volcanic forcing on the ENSO–Indian monsoon coupling, Science Advances, 6, eaba8164 (2020). DOI:10.1126/sciadv.aba8164
  • T. Westerhold, N. Marwan, A. J. Drury, D. Liebrand, C. Agnini, E. Anagnostou, J. S. K. Barnet, S. M. Bohaty, D. De Vleeschouwer, F. Florindo, T. Frederichs, D. A. Hodell, A. E. Holbourn, D. Kroon, V. Lauretano, K. Littler, L. J. Lourens, M. Lyle, H. Pälike, U. Röhl, J. Tian, R. H. Wilkens, P. A. Wilson and J. C. Zachos: An astronomically dated record of Earth's climate and its predictability over the last 66 million years, Science, 369(6509), 1383–1387 (2020). DOI:10.1126/science.aba6853
  • S. M. Vallejo-Bernal, T. Braun, N. Marwan and J. Kurths: PIKART: A Comprehensive Global Catalog of Atmospheric Rivers, Journal of Geophysical Research: Atmospheres, 130(15), e2024JD041869 (2025). DOI:10.1029/2024JD041869

Cardiovascular systems

Besides the main focus on climate related problems, recurrence properties of the cardiovascular system are studied, e.g., to early detect ventricular tachycardia or preeclampsia, or to investigate the coupling mechanisms in the cardio-respiratory system.

  • N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan and J. Kurths: Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data, Physical Review E, 66(2), 026702 (2002). DOI:10.1103/PhysRevE.66.026702
  • N. Marwan, Y. Zou, N. Wessel, M. Riedl and J. Kurths: Estimating coupling directions in the cardio-respiratory system using recurrence properties, Philosophical Transactions of the Royal Society A, 371(1997), 20110624 (2013). DOI:10.1098/rsta.2011.0624
  • G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, H. Stepan, J. Kurths, T. Walther and N. Wessel: Classifying healthy women and preeclamptic patients from cardiovascular data using recurrence and complex network methods, Autonomic Neuroscience, 178(1–2), 103–110 (2013). DOI:10.1016/j.autneu.2013.05.003

Neuroscience

Further interest in life science is related to EEG analysis, aiming at the detection of event related potentials or early signatures of epileptic seizures, or identifying pathological changes in brains connectivity due to diseases.

  • N. Marwan and A. Meinke: Extended recurrence plot analysis and its application to ERP data, International Journal of Bifurcation and Chaos, 14(2), 761–771 (2004). DOI:10.1142/S0218127404009454
  • S. Schinkel, N. Marwan and J. Kurths: Order patterns recurrence plots in the anaylsis of ERP data, Cognitive Neurodynamics, 1(4), 317–325 (2007). DOI:10.1007/s11571-007-9023-z
  • S. Schinkel, N. Marwan and J. Kurths: Brain signal analysis based on recurrences, Journal of Physiology-Paris, 103(6), 315–323 (2009). DOI:10.1016/j.jphysparis.2009.05.007
  • E. J. Ngamga, S. Bialonski, N. Marwan, J. Kurths, C. Geier and K. Lehnertz: Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data, Physics Letters A, 380(16), 1419–1425 (2016). DOI:10.1016/j.physleta.2016.02.024
  • M. Mannone, P. Fazio and N. Marwan: Modeling a neurological disorder as the result of an operator acting on the brain: A first sketch based on network channel modeling, Chaos, 34, 053133 (2024). DOI:10.1063/5.0199988
3D microCT image of trabecular bone

3D image analysis

Methods to investigate complexity in 3D have been applied to study structural changes in trabecular bone, such as occurring during osteoporosis or space flights.

  • N. Marwan, P. Saparin and J. Kurths: Measures of complexity for 3D image analysis of trabecular bone, European Physical Journal – Special Topics, 143(1), 109–116 (2007). DOI:10.1140/epjst/e2007-00078-x
  • N. Marwan, J. Kurths, J. S. Thomsen, D. Felsenberg and P. Saparin: Three dimensional quantification of structures in trabecular bone using measures of complexity, Physical Review E, 79(2), 021903 (2009). DOI:10.1103/PhysRevE.79.021903
  • T. Schmah, N. Marwan, J. S. Thomsen and P. Saparin: Long range node-strut analysis of trabecular bone microarchitecture, Medical Physics, 38(9), 5003–5011 (2011). DOI:10.1118/1.3622600

>Cave research

Speleology

Scientific research in caves is performed to explore and survey newly discovered cave parts, but also to collect data for the palaeoclimate studies (samples, monitoring). Cave research is focused on caves in Switzerland (research with ISAAK), but also in India, Caucasus, Kosovo, and Germany.

  • N. Marwan: Cave Blisters in der Oberländerhöhle (M3)/ Découverte de blisters dans la Oberländerhöhle (M3), Stalactite, 50(2), 103–105 (2000)
  • N. Marwan: Kalzit-Sinter in Sandsteinhöhlen des Elbsandsteingebirges, Die Höhle, 51(1), 19-20 (2000)
  • N. Marwan: Das Karstgebiet des Bol'šoj Tha\v c, Abhandlungen und Berichte des Naturkundemuseums Görlitz, 79(1), 55-84 (2007)
  • S. Breitenbach, N. Marwan and G. Wibbelt: Weißnasensyndrom in Nordamerika – Pilzbesiedlung in Europa, Nyctalus, 16(3), 172–179 (2011)
  • N. Marwan: Der digitale Sägistal-Kataster, Stalactite, 73(1), 24–33 (2023)
  • S. F. M. Breitenbach and N. Marwan: Using Low-Cost Software to Obtain and Study Stalagmite Greyscale Data, CREG Journal, 125, 7–10 (2024)

>Projects & grants

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