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The following toolboxes for modelling of dynamical systems and time series analysis were developed in the Interdisciplinary Center for Dynamics of Complex Systems Potsdam, the Cardiovascular Physics Group at the Humboldt-Universität zu Berlin, and the Potsdam Institute for Climate Impact Research (PIK):

• ACE – Nonlinear Regression Analysis
  Voss, H., Kurths, J.: Reconstruction of nonlinear time delay models from data by the use of optimal transformations, Phys. Lett. A, 234, 1997, 336-344, doi:10.1016/S0375-9601(97)00598-7.
  Voss, H., Kolodner, P., Abel, M., Kurths, J.: Amplitude equations from spatiotemporal binary-fluid convection data. Phys. Rev. Lett., 83(17), 1999, 3422-3425, doi:10.1103/PhysRevLett.83.3422.

• Adaptive Filtering Procedure
  Wessel, N., Voss, A., Malberg, H., Ziehmann, Ch., Voss, H. U., Schirdewan, A., Meyerfeldt, U., Kurths, J.: Nonlinear analysis of complex phenomena in cardiological data, Herzschr. Elektrophys., 11(3), 2000, 159-173, doi:10.1007/s003990070035.

• CoinCalc – Toolbox for estimation of event coincidences
  Siegmund, J. F., Siegmund, N., Donner, R. V.: CoinCalc – A new R package for quantifyung simultaneities of event series, Computers & Geosciences, 98, 2017, 64. doi:10.1016/j.cageo.2016.10.004.

• COPRA – Constructing Proxy Records From Age Models (Ver , last mod. )
  Breitenbach, S. F. M., Rehfeld, K., Goswami, B., Baldini, J. U. L., Ridley, H. E., Kennett, D., Prufer, K., Aquino, V. V., Asmerom, Y., Polyak, V. J., Cheng, H., Kurths, J., Marwan, N.: COnstructing Proxy Records from Age models (COPRA), Climate of the Past, 8, 2012, 1765-1779 doi:10.5194/cp-8-1765-2012.

• Commandline Recurrence Plots (Ver 1.13z, last mod. 2006-03-08)
  Marwan, N., Romano, M. C., Thiel, M., Kurths, J.: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5-6), 2007, 237-329, doi:10.1016/j.physrep.2006.11.001.
  

• Cross Recurrence Plot Toolbox (Ver 5.24 (R34), last mod. 09-Mar-2022 21:21:16)
  Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J.: Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data, Phys. Rev. E, 66(2), 2002, 026702, doi:10.1103/PhysRevE.66.026702.
  Marwan, N., Thiel, M., Nowaczyk, N. R.: Cross Recurrence Plot Based Synchronization of Time Series, Nonlin. Proc. Geophys., 9, 2002, 325-331, url:www.copernicus.org/EGU/npg/9/325.htm.
  Marwan, N., Kurths, J.: Nonlinear analysis of bivariate data with cross recurrence plots, Phys. Lett. A, 302(5-6), 2002, 299-307, doi:10.1016/S0375-9601(02)01170-2.
  Marwan, N., Romano, M. C., Thiel, M., Kurths, J.: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5-6), 2007, 237-329, doi:10.1016/j.physrep.2006.11.001.
  Schinkel, S., Marwan, N., Dimigen, O. Kurths, J.: Confidence Bounds of recurrence-based complexity measures, Physics Letters A, 373(26), 2009, 2245-2250, doi:10.1016/j.physleta.2009.04.045.

• Identification of Coupling Direction
  Rosenblum, M. G., Cimponeriu, L., Bezerianos, A., Patzak, A. and Mrowka, R.: Identification of coupling direction: Application to cardiorespiratory interaction, Phys. Rev. E, 65, 2002, 041909, doi:10.1103/PhysRevE.65.041909.

• Inner Composition Alignment (IOTA)
  Hempel, S., Koseska, A., Kurths, J., Nikoloski, Z.: Inner Composition Alignment for Inferring Directed Networks from Short Time Series, Phys. Rev. Lett., 107(5), 054101, 2011, doi:10.1103/PhysRevLett.107.054101
  Hempel, S., Koseska, A., Nikoloski, Z.: Data-driven reconstruction of directed networks, Europ. Phys. J. B, 86, 250, 2013, doi:10.1140/epjb/e2013-31111-8

• K2 - Dynamical Invariants by Recurrence Plots
  Thiel, M., Romano, M. C., J. Kurths, J.: Analytical Description of Recurrence Plots of white noise and chaotic processes, Izvestija vyssich ucebnych zavedenij/ Prikladnaja nelinejnaja dinamika - Applied Nonlinear Dynamics, 11(3), 2003, 20-30.
  Marwan, N., Romano, M. C., Thiel, M., Kurths, J.: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5-6), 2007, 237-329, 10.1016/j.physrep.2006.11.001.

• NEST ‐ Toolbox for the analysis of non-equidistantly sampled time series
  Rehfeld, K., Marwan, N., Heitzig, J., Kurths, J.: Comparison of correlation analysis techniques for irregularly sampled time series, Nonlin. Proc. Geophys., 18(3), 389-404, 2011.
  Rehfeld, K., Kurths, J.: Similarity measures for irregular and age uncertain time series, Clim. Past., 10, 107-122, 2014.
  

• DS Prolog
  Hübner, S.: Wissensbasierte Modellierung von Klassifikatoren für Zeit-Frequenz-Muster in PCM-Daten, Logos Verlag, Berlin, ISBN 978-3-8325-1596-6, 2007.

• PECUZAL for MATLAB, Julia, and Python
  Kraemer, K. H., Datseris, G., Kurths, J., Kiss, I. Z., Ocampo-Espindola, J. L., Marwan, N.: A unified and automated approach to attractor reconstruction, New J. Phys., 23(3), 033017, doi:10.1088/1367-2630/abe336.
  

• Permutation Entropy
  Riedl, M., Müller, A., Wessel, N.: Practical considerations of permutation entropy, Eur. Phys. J. ST, 222(2), 249-262, 2013.
  

• pyunicorn ‐ UNIfied COmplex Network and Recurrence aNalysis toolbox
  Donges, J. F., Heitzig, J., Beronov, B., Wiedermann, M., Runge, J., Feng, Q. Y., … Kurths, J.: Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos, 25(11), 113101, 2015, doi:10.1063/1.4934554.
  

• Recurrence Plots for MATLAB
  Trauth, M. H., Asrat, A., Duesing, W., Foerster, V., Kraemer, K. H., Marwan, N., Maslin, M. A., Schaebitz, F.: Classifying past climate change in the Chew Bahir basin, southern Ethiopia, using recurrence quantification analysis, Clim. Dyn., 53(5), 2557–2572, 2019, doi:10.1007/s00382-019-04641-3.
  

• Recurrence Structure Analysis
  Hutt, A., beim Graben, P.: Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data, Front. Appl. Math. Stat., 3, 11, 2017, doi:10.3389/fams.2017.00011.
  

• Symbolic Dynamics from Recurrence Plots
  beim Graben, P., Hutt, A.: Detecting recurrence domains of dynamical systems by symbolic dynamics, Phys. Rev. Lett., 110, 154101, 2013, doi:10.1103/PhysRevLett.110.154101.
  

• System Identification Tool (Ver 1.6.1 (R9.3b), last mod. 25-Feb-2008 12:34:15)
  Sitz, A., Schwarz, U., Kurths, J., Voss, H. U.: Estimation of parameters and unobserved components for nonlinear systems from noisy time series, Phys. Rev. E, 66, 2002, 016210, doi:10.1103/PhysRevE.66.016210.

• TIGRAMITE ‐ Time Series Graph and Momentary Information Transfer Estimation
  Runge, J., Heitzig, J., Marwan, N., Kurths, J.: Quantifying Causal Coupling Strength: A Lag-specific Measure For Multivariate Time Series Related To Transfer Entropy, Physical Review E, 86, 2012, 061121.
  Runge, J., Heitzig, J., Petoukhov, V., Kurths, J.: Escaping the Curse of Dimensionality in Estimating Multivariate Transfer Entropy, Physical Review Letters, 108, 2012, 258701.
  

• SOWAS – Wavelet Spectral and Coherence Analysis
  Maraun, D., Kurths, J.: Cross Wavelet Analysis. Significance Testing and Pitfalls, Nonlin. Proc. Geoph., 11, 2004, 505-514, doi:10.5194/npg-11-505-2004.

If you use data, software or other stuff from this web site, please cite the corresponding publication and this web site (tocsy.pik-potsdam.de)!

Information and contact:
Norbert Marwan

The authors of the programmes are responsible for their submissions.

last modified: 2022-03-29, 09:24:19