@article{TrauthAsratDuesingetal.2019,
  author    = {Trauth, Martin H. and Asrat, Asfawossen and D{\"u}sing, Walter and Foerster, Verena and Kr{\"a}mer, K. Hauke and Marwan, Norbert and Maslin, Mark A. and Sch{\"a}bitz, Frank},
  title     = {Classifying past climate change in the Chew Bahir basin, southern Ethiopia, using recurrence quantification analysis},
  series = {Climate dynamics : observational, theoretical and computational research on the climate system},
  volume    = {53},
  journal   = {Climate dynamics : observational, theoretical and computational research on the climate system},
  number    = {5-6},
  publisher = {Springer},
  address   = {New York},
  issn      = {0930-7575},
  doi       = {10.1007/s00382-019-04641-3},
  pages     = {2557 -- 2572},
  year      = {2019},
  abstract  = {The Chew Bahir Drilling Project (CBDP) aims to test possible linkages between climate and evolution in Africa through the analysis of sediment cores that have recorded environmental changes in the Chew Bahir basin. In this statistical project we consider the Chew Bahir palaeolake to be a dynamical system consisting of interactions between its different components, such as the waterbody, the sediment beneath lake, and the organisms living within and around the lake. Recurrence is a common feature of such dynamical systems, with recurring patterns in the state of the system reflecting typical influences. Identifying and defining these influences contributes significantly to our understanding of the dynamics of the system. Different recurring changes in precipitation, evaporation, and wind speed in the Chew Bahir basin could result in similar (but not identical) conditions in the lake (e.g., depth and area of the lake, alkalinity and salinity of the lake water, species assemblages in the water body, and diagenesis in the sediments). Recurrence plots (RPs) are graphic displays of such recurring states within a system. Measures of complexity were subsequently introduced to complement the visual inspection of recurrence plots, and provide quantitative descriptions for use in recurrence quantification analysis (RQA). We present and discuss herein results from an RQA on the environmental record from six short (< 17 m) sediment cores collected during the CBDP, spanning the last 45 kyrs. The different types of variability and transitions in these records were classified to improve our understanding of the response of the biosphere to climate change, and especially the response of humans in the area.},
  language  = {en}
}
@misc{Marwan2011,
  author    = {Marwan, Norbert},
  title     = {How to avoid potential pitfalls in recurrence plot based data analysis},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {21},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {4},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127411029008},
  pages     = {1003 -- 1017},
  year      = {2011},
  abstract  = {Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.},
  language  = {en}
}
@phdthesis{Marwan2019,
  author    = {Marwan, Norbert},
  title     = {Recurrence plot techniques for the investigation of recurring phenomena in the system earth},
  isbn      = {978-3-00-064508-2},
  doi       = {10.25932/publishup-44197},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-441973},
  school      = {Universit{\"a}t Potsdam},
  pages     = {ix, 254},
  year      = {2019},
  abstract  = {The habilitation deals with the numerical analysis of the recurrence properties of geological and climatic processes. The recurrence of states of dynamical processes can be analysed with recurrence plots and various recurrence quantification options. In the present work, the meaning of the structures and information contained in recurrence plots are examined and described. New developments have led to extensions that can be used to describe the recurring patterns in both space and time. Other important developments include recurrence plot-based approaches to identify abrupt changes in the system's dynamics, to detect and investigate external influences on the dynamics of a system, the couplings between different systems, as well as a combination of recurrence plots with the methodology of complex networks. Typical problems in geoscientific data analysis, such as irregular sampling and uncertainties, are tackled by specific modifications and additions. The development of a significance test allows the statistical evaluation of quantitative recurrence analysis, especially for the identification of dynamical transitions. Finally, an overview of typical pitfalls that can occur when applying recurrence-based methods is given and guidelines on how to avoid such pitfalls are discussed. In addition to the methodological aspects, the application potential especially for geoscientific research questions is discussed, such as the identification and analysis of transitions in past climates, the study of the influence of external factors to ecological or climatic systems, or the analysis of landuse dynamics based on remote sensing data.},
  language  = {en}
}
@article{WendiMarwanMerz2018,
  author    = {Wendi, Dadiyorto and Marwan, Norbert and Merz, Bruno},
  title     = {In Search of Determinism-Sensitive Region to Avoid Artefacts in Recurrence Plots},
  series = {International journal of bifurcation and chaos : in applied sciences and engineering},
  volume    = {28},
  journal   = {International journal of bifurcation and chaos : in applied sciences and engineering},
  number    = {1},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0218-1274},
  doi       = {10.1142/S0218127418500074},
  pages     = {15},
  year      = {2018},
  abstract  = {As an effort to reduce parameter uncertainties in constructing recurrence plots, and in particular to avoid potential artefacts, this paper presents a technique to derive artefact-safe region of parameter sets. This technique exploits both deterministic (incl. chaos) and stochastic signal characteristics of recurrence quantification (i.e. diagonal structures). It is useful when the evaluated signal is known to be deterministic. This study focuses on the recurrence plot generated from the reconstructed phase space in order to represent many real application scenarios when not all variables to describe a system are available (data scarcity). The technique involves random shuffling of the original signal to destroy its original deterministic characteristics. Its purpose is to evaluate whether the determinism values of the original and the shuffled signal remain closely together, and therefore suggesting that the recurrence plot might comprise artefacts. The use of such determinism-sensitive region shall be accompanied by standard embedding optimization approaches, e.g. using indices like false nearest neighbor and mutual information, to result in a more reliable recurrence plot parameterization.},
  language  = {en}
}