# > Methods to study complex systems

related to PIK research on Time Series Analysis and Complex Networks

## Recurrence plots

*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, or complex network based quantification.

**N. Marwan, M. C. Romano, M. Thiel, 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, 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, J. Kurths**: Recurrence plots 25 years later – Gaining confidence in dynamical transitions, Europhysics Letters,**101**, 20007 (2013). DOI:10.1209/0295-5075/101/20007

## Complex networks

*Complex networks* provide a powerful approach
to investigate extended and spatio-temporal systems, such as the climate by *climate networks*.
Moreover, they offer an alternative way for a recurrence based time-series analysis by *recurrence
networks*.

**K. Rehfeld, N. Marwan, S. F. M. Breitenbach, 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. Boers, B. Bookhagen, N. Marwan, J. Kurths, 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**N. Marwan, J. Kurths**: Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems, Chaos,**25**, 097609 (2015). DOI:10.1063/1.4916924**Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, 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

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, 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, 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, J. Kurths**: See-saw relationship of the Holocene East Asian-Australian summer monsoon, Nature Communications,**7**, 12929 (2016). DOI:10.1038/ncomms12929**I. Ozken, D. Eroglu, S. F. M. Breitenbach, N. Marwan, L. Tan, U. Tirnakli, J. Kurths**: Recurrence plot analysis of irregularly sampled data, Physical Review E,**98**, 052215 (2018). DOI:10.1103/PhysRevE.98.052215**B. Goswami, N. Boers, A. Rheinwalt, N. Marwan, J. Heitzig, S. F. M. Breitenbach, J. Kurths**: Abrupt transitions in time series with uncertainties, Nature Communications,**9**, 48 (2018). DOI:10.1038/s41467-017-02456-6

# > Complexity in applications

## Climate and palaeoclimate

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.

**J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, 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*Science cover story:***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, 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, 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**T. Westerhold, N. Marwan, et al.**: 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**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, J. Kurths**: Fingerprint of volcanic forcing on the ENSO-Indian monsoon coupling, Science Advances,**6**, eaba8164 (2020). DOI:10.1126/sciadv.aba8164

## 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, 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**G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, H. Stepan, J. Kurths, T. Walther, 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**N. Marwan, Y. Zou, N. Wessel, M. Riedl, 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

## EEG analysis

Further interest in life science is related to *EEG analysis*, aiming at the detection
of event related potentials or early signatures of epileptic seizures.

**N. Marwan, 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, 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, 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, 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

## 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, 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, 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, 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

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**: Das Karstgebiet des Bol'soj Thac, Abhandlungen und Berichte des Naturkundemuseums Görlitz,**79**(1), 55-84 (2007).**S. Breitenbach, N. Marwan, G. Wibbelt**: Weißnasensyndrom in Nordamerika – Pilzbesiedlung in Europa, Nyctalus,**16**(3), 172-179 (2011).one of the first web presentations of speleology was the speleo server east

# > Projects & grants

2000-2003

DFG SPP 1097: Erdmagnetische Variationen: Nonlinear Phase and Correlation Analysis of Palaeomagnetic and Palaeoclimatic Records2003-2005

ESA project AO-99-030: 2D and 3D Quantification of Bone Structure and its Changes in Microgravity Condition by Measures of Complexity2005-2008

ESA project AO-2004-125: Assessing the Influence of Microarchitecture on the Mechanical Performance of Bone and its Changes in Microgravity from in-vivo Measurements2006-2015

DFG Graduate School GK 1364: Shaping Earth's surface in a variable environment2010

Volkswagen Foundation I/85 116: International Workshop on Recent Achievements on the Study of Extreme Events2010-2013

WGL SAW-2010: Evolving Complex Networks (ECONS) — Regional resource management under environmental and demographic change2011-2014

DFG Graduate School GK 1539: Sichtbarkeit und Sichtbarmachung, Hybride Formen des Bildwissens2011-2013

DFG Research Group FOR 1380: Himalaya: Modern and Past Climates (HIMPAC): Analysis of the dynamics of palaeo and modern climate data under consideration of dating errors focussed on climate transitions and interrelations between teleconnections and regional climate2011-2013

DFG project KU837/34-1: Interactions and complex structures in the dynamics of changing climate: impact of tipping elements in presence and past2011-2014

BMBF Spitzenforschung und Innovation in den Neuen Ländern: Potsdam Research Cluster for Georisk Analysis, Environmental Change and Sustainability (PROGRESS): Extremereignisse in Geoarchiven2013-2016

WGL SAW-2013-IZW-2: Gradual environmental change versus single catastrophe — Identifying drivers of mammalian evolution2014-2015

DFG project MA 4759/4-1: Investigation of past and present climate dynamics and its stability by means of a spatio-temporal analysis of climate data using complex networkssince 2015

DFG Graduate School GK 2043: Natural Hazards and Risks in a Changing World (NatRiskChange)2016-2020

EU project QUEST (H2020-MSCA-RISE-2015): QUantitative palaeoEnvironments from SpeleoThems (QUEST)2017-2019

DFG project 337352542: Trends, rhythms and events in East African climate: statistical analysis of the paleoclimare records of the long sediment cores of the Chew Bahir basin2017-2022

DFG project MA4759/8-1: Impacts of uncertainties in climate data analyses (IUCliD): Approaches to working with measurements as a series of probability distributions2017-2020

DFG project MA4759/9-1: Recurrence plot analysis of regime changes in dynamical systemssince 2019

DFG project MA4759/11-1: Nonlinear empirical mode analysis of complex systems: Development of general approach and application in climatesince 2019

EU project TiPES: Tipping points in the earth systemsince 2020

BMBF project climXtreme: A research network on climate change and extreme eventssince 2022

DFG project MA 4759/18-1: Testing the isothermal thermoluminescence dating method to constrain mid-Pleistocene speleothem growth phases in the Bleßberg Cave2023

DFG project MA 4759/19-1: International scientific conference: „Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives (NDA23)“, Potsdam2023

geo.X grant*Grow Your Idea!*: Geo.X Brainstorm Meeting: „Reconstructing Environmental Changes in the Swiss Alps“, Potsdam