@article{DongesZouMarwanetal.2009, author = {Donges, Jonathan Friedemann and Zou, Yong and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Complex networks in climate dynamics : comparing linear and nonlinear network construction methods}, issn = {1951-6355}, doi = {10.1140/epjst/e2009-01098-2}, year = {2009}, abstract = {Complex network theory provides a powerful framework to statistically investigate the topology of local and non- local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.}, language = {en} } @article{SchinkelMarwanDimigenetal.2009, author = {Schinkel, Stefan and Marwan, Norbert and Dimigen, Olaf and Kurths, J{\"u}rgen}, title = {Confidence bounds of recurrence-based complexity measures}, issn = {0375-9601}, doi = {10.1016/j.physleta.2009.04.045}, year = {2009}, abstract = {In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real- life data.}, language = {en} } @article{ZolotovaPonyavinMarwanetal.2009, author = {Zolotova, Nadezhda V. and Ponyavin, Dmitri I. and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Long-term asymmetry in the wings of the butterfly diagram}, issn = {0004-6361}, doi = {10.1051/0004-6361/200811430}, year = {2009}, abstract = {Aims. Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles. Methods. We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots. Results. We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.}, language = {en} } @article{SchinkelMarwanKurths2009, author = {Schinkel, Stefan and Marwan, Norbert and Kurths, J{\"u}rgen}, title = {Brain signal analysis based on recurrences}, issn = {0928-4257}, doi = {10.1016/j.jphysparis.2009.05.007}, year = {2009}, abstract = {The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to Such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.}, language = {en} } @article{GoswamiMarwanFeulneretal.2013, author = {Goswami, Bedartha and Marwan, Norbert and Feulner, Georg and Kurths, J{\"u}rgen}, title = {How do global temperature drivers influence each other?}, series = {European physical journal special topics}, volume = {222}, journal = {European physical journal special topics}, number = {3-4}, publisher = {Springer}, address = {Heidelberg}, issn = {1951-6355}, doi = {10.1140/epjst/e2013-01889-8}, pages = {861 -- 873}, year = {2013}, abstract = {We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations.}, language = {en} } @article{MarwanBellerFelsenbergetal.2012, author = {Marwan, Norbert and Beller, Gise and Felsenberg, Dieter and Saparin, Peter and Kurths, J{\"u}rgen}, title = {quantifying changes in the spatial structure of trabecular bone}, series = {International journal of bifurcation and chaos : in applied sciences and engineering}, volume = {22}, journal = {International journal of bifurcation and chaos : in applied sciences and engineering}, number = {2}, publisher = {World Scientific}, address = {Singapore}, issn = {0218-1274}, doi = {10.1142/S0218127412500277}, pages = {12}, year = {2012}, abstract = {We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization.}, language = {en} } @article{ErogluMarwanPrasadetal.2014, author = {Eroglu, Deniz and Marwan, Norbert and Prasad, Sushma and Kurths, J{\"u}rgen}, title = {Finding recurrence networks' threshold adaptively for a specific time series}, series = {Nonlinear processes in geophysics}, volume = {21}, journal = {Nonlinear processes in geophysics}, number = {6}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1023-5809}, doi = {10.5194/npg-21-1085-2014}, pages = {1085 -- 1092}, year = {2014}, abstract = {Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches - recurrence plots and recurrence networks -, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.}, language = {en} } @article{GoswamiHeitzigRehfeldetal.2014, author = {Goswami, Bedartha and Heitzig, Jobst and Rehfeld, Kira and Marwan, Norbert and Anoop, Ambili and Prasad, Sushma and Kurths, J{\"u}rgen}, title = {Estimation of sedimentary proxy records together with associated uncertainty}, series = {Nonlinear processes in geophysics}, volume = {21}, journal = {Nonlinear processes in geophysics}, number = {6}, publisher = {Copernicus}, address = {G{\"o}ttingen}, issn = {1023-5809}, doi = {10.5194/npg-21-1093-2014}, pages = {1093 -- 1111}, year = {2014}, abstract = {Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record. We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age-depth and proxy-depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India. Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation.}, language = {en} } @article{DongesDonnerTrauthetal.2011, author = {Donges, Jonathan Friedemann and Donner, Reik Volker and Trauth, Martin H. and Marwan, Norbert and Schellnhuber, Hans Joachim and Kurths, J{\"u}rgen}, title = {Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution}, series = {Proceedings of the National Academy of Sciences of the United States of America}, volume = {108}, journal = {Proceedings of the National Academy of Sciences of the United States of America}, number = {51}, publisher = {National Acad. of Sciences}, address = {Washington}, issn = {0027-8424}, doi = {10.1073/pnas.1117052108}, pages = {20422 -- 20427}, year = {2011}, abstract = {Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B. P.), (ii) Early Pleistocene (2.25-1.6 Ma B. P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B. P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.}, language = {en} } @article{MarwanSchinkelKurths2013, author = {Marwan, Norbert and Schinkel, Stefan and Kurths, J{\"u}rgen}, title = {Recurrence plots 25 years later -Gaining confidence in dynamical transitions}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {101}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {2}, publisher = {EDP Sciences}, address = {Mulhouse}, issn = {0295-5075}, doi = {10.1209/0295-5075/101/20007}, pages = {6}, year = {2013}, abstract = {Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos-chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature. This paper is dedicated to the 25th anniversary of the introduction of recurrence plots.}, language = {en} }