ACE - Nonlinear Regression Analysis

An application of the ACE algorithm of Breiman and Friedman (1985) in nonlinear dynamics.

• H. Voss, J. Kurths, "Reconstruction of nonlinear time delay models from data by the use of optimal transformations", Physics Letters A, vol. 234, 1997, pp. 336–344. doi:10.1016/S0375-9601(97)00598-7
• H. Voss, P. Kolodner, M. Abel, J. Kurths, "Amplitude equations from spatiotemporal binary-fluid convection data", Physical Review Letters, vol. 83, no. 17, 1999, pp. 3422–3425. doi:10.1103/PhysRevLett.83.3422

ADA - Adaptive Filtering Procedure

An adaptive filtering procedure regarding sudden changes in time series.

• N. Wessel, A. Voss, H. Malberg, C. Ziehmann, H. U. Voss, A. Schirdewan, U. Meyerfeldt, J. Kurths, "Nonlinear analysis of complex phenomena in cardiological data", Herzschr. Elektrophys., vol. 11, no. 3, 2000, pp. 159–173. doi:10.1007/s003990070035

apRQA - Approximate Recurrence Quantification Analysis

Julia package to calculate selected main measures of the recurrence quantification analysis (RQA). The calculation is performed in an highly efficient but very approximative way using the algorithm described in Spiegel et al, 2016.

• S. Spiegel, D. Schultz and N. Marwan, "Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice", in Recurrence Plots and Their Quantifications: Expanding Horizons, J. C. L. Webber, C. Ioana, N. Marwan, Eds., Cham: Springer, 2016, pp. 113–136. doi:10.1007/978-3-319-29922-8_6

CoinCalc - Event Coincidence Analysis

Toolbox for estimation of event Coincidences.

• J. F. Siegmund, N. Siegmund and R. V. Donner, "CoinCalc – A new R package for quantifying simultaneities of event series", Computers & Geosciences, vol. 98, 2017, pp. 64. doi:10.1016/j.cageo.2016.10.004

Commandline Recurrence Plots

Project page for commandline recurrence plot programme.

• N. Marwan, M. C. Romano, M. Thiel, J. Kurths, "Recurrence Plots for the Analysis of Complex Systems", Physics Reports, vol. 438, no. 5–6, 2007, pp. 237–329. doi:10.1016/j.physrep.2006.11.001

COPRA - Constructing Proxy Records From Age Models

Toolbox for age modelling.

• 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, vol. 8, 2012, pp. 1765–1779. doi:10.5194/cp-8-1765-2012

Coupling analysis of transient dynamics

Coupling analysis of transient dynamics for ensemble data.

• A. Mueller, M. Riedl, T. Penzel, J. Kurths, N. Wessel, "Kardiorespiratorische Koordination und Ensemble-Kopplungsspuren zur ereignisbasierten Charakterisierung kardiovaskulärer Interaktionen während des Schlafes", Somnologie, vol. 18, 2014, pp. 243–251.
• A. Mueller, M. Riedl, T. Penzel, H. Bonnemeier, J. Kurths, e. al., "Coupling analysis of transient cardiovascular dynamics", Biomed. Tech., vol. 58, 2013, pp. 131–139.
• N. Wessel, A. Suhrbier, M. Riedl, N. Marwan, H. Malberg, e. al., "Detection of time-delayed interactions in biosignals using symbolic coupling traces", Europhys. Lett., vol. 87, 2009, pp. 10004.

Cross Recurrence Plot Toolbox

A MATLAB toolbox for computing recurrence plots, cross recurrence plots and their quantifications.

• 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, vol. 66, no. 2, 2002, pp. 026702. doi:10.1103/PhysRevE.66.026702
• N. Marwan, M. Thiel and N. R. Nowaczyk, "Cross Recurrence Plot Based Synchronization of Time Series", Nonlinear Processes in Geophysics, vol. 9, no. 3/4, 2002, pp. 325–331. doi:10.5194/npg-9-325-2002
• N. Marwan, J. Kurths, "Nonlinear analysis of bivariate data with cross recurrence plots", Physics Letters A, vol. 302, no. 5–6, 2002, pp. 299–307. doi:10.1016/S0375-9601(02)01170-2
• N. Marwan, M. C. Romano, M. Thiel, J. Kurths, "Recurrence Plots for the Analysis of Complex Systems", Physics Reports, vol. 438, no. 5–6, 2007, pp. 237–329. doi:10.1016/j.physrep.2006.11.001
• S. Schinkel, N. Marwan, O. Dimigen, J. Kurths, "Confidence bounds of recurrence-based complexity measures", Physics Letters A, vol. 373, no. 26, 2009, pp. 2245–2250. doi:10.1016/j.physleta.2009.04.045

DSProlog - Knowledge discovery support environment (KDSE)

Experimental knowledge discovery support environment for knowledge discovery in PCM-data.

• S. Hübner, Wissensbasierte Modellierung von Klassifikatoren für Zeit-Frequenz-Muster in PCM-Daten, Berlin: Logos Verlag, 2007.

Identification of Coupling Direction.

A Matlab programme for identification of coupling direction.

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

IOTA - Inner composition alignment

Permutation-based association measure to detect regulatory links from very short time series

• S. Hempel, A. Koseska, J. Kurths, Z. Nikoloski, "Inner Composition Alignment for Inferring Directed Networks from Short Time Series", Phys. Rev. Lett., vol. 107, no. 5, 2011, pp. 054101. doi:10.1103/PhysRevLett.107.054101
• S. Hempel, A. Koseska and Z. Nikoloski, "Data-driven reconstruction of directed networks", European Phys. J. B, vol. 86, 2013, pp. 250. doi:10.1140/epjb/e2013-31111-8

K2 - Dynamical Invariants by Recurrence Plots

Online calculation of the K2 entropy by means of recurrence plots.

• M. Thiel, M. C. Romano and J. Kurths, "Analytical Description of Recurrence Plots of white noise and chaotic processes", Applied Nonlinear Dynamics/ Izvestiya Vysshikh Uchebnykh Zavedeniy – Prikladnaya Nelineynaya Dinamika, vol. 11, no. 3, 2003, pp. 20–30. doi:10.18500/0869-6632-2003-11-3-20-30
• N. Marwan, M. C. Romano, M. Thiel, J. Kurths, "Recurrence Plots for the Analysis of Complex Systems", Physics Reports, vol. 438, no. 5–6, 2007, pp. 237–329. doi:10.1016/j.physrep.2006.11.001

MAKEINSTALL for MATLAB

The easy way of distributing MATLAB toolboxes.

NEST – Toolbox for the analysis of non-equidistantly sampled time series

Toolbox for the analysis of non-equidistantly sampled time series.

• K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths, "Comparison of correlation analysis techniques for irregularly sampled time series", Nonlinear Processes in Geophysics, vol. 18, no. 3, 2011, pp. 389–404. doi:10.5194/npg-18-389-2011
• K. Rehfeld, J. Kurths, "Similarity measures for irregular and age uncertain time series", Clim. Past, vol. 10, 2014, pp. 107–122.

PECUZAL Attractor Reconstruction

Automatic phase space reconstruction method.

• K. H. Kraemer, G. Datseris, J. Kurths, I. Z. Kiss, J. L. {Ocampo-Espindola}, N. Marwan, "A unified and automated approach to attractor reconstruction", New Journal of Physics, vol. 23, 2021, pp. 033017. doi:10.1088/1367-2630/abe336

PETROPY - Permutation Entropy

Simple and robust method to estimate complextity of time series.

• M. Riedl, A. Müller and N. Wessel, "Practical considerations of permutation entropy", Eur. Phys. J. ST, vol. 222, no. 2, 2013, pp. 249–262.

pyUnicorn - UNIfied COmplex Network and Recurrence aNalysis toolbox

Object-oriented python package for advanced analysis and modeling of complex networks and recurrence analysis.

• J. F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q. Y. Feng, L. Tupikina, V. Stolbova, R. V. Donner, N. Marwan, H. A. Dijkstra, J. Kurths, "Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package", Chaos, vol. 25, 2015, pp. 113101. doi:10.1063/1.4934554

RECFLOW - Recurrence flow

Package for calculating recurrence flow.

• T. Braun, K. H. Kraemer and N. Marwan, "Recurrence flow measure of nonlinear dependence", European Physical Journal – Special Topics, vol. 232, 2023, pp. 57–67. doi:10.1140/epjs/s11734-022-00687-3

RECGRAM – Symbolic Dynamics from Recurrence Plots

Symbolic Dynamics from Recurrence Plots.

• P. b. Graben, A. Hutt, "Detecting Recurrence Domains of Dynamical Systems by Symbolic Dynamics", Physical Review Letters, vol. 110, no. 15, 2013, pp. 154101. doi:10.1103/PhysRevLett.110.154101

RECLAC - Recurrence lacunarity

Package for calculating recurrence lacunarity.

• T. Braun, V. R. Unni, R. I. Sujith, J. Kurths, N. Marwan, "Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure", Nonlinear Dynamics, vol. 104, 2021, pp. 3955–3973. doi:10.1007/s11071-021-06457-5

Recurrence Plots for MATLAB

Simple MATLAB scripts for computing recurrence plots and their quantifications.

• M. H. Trauth, A. Asrat, W. Duesing, V. Foerster, K. H. Kraemer, N. Marwan, M. A. Maslin, F. Sch\"abitz, "Classifying past climate change in the Chew Bahir basin, southern Ethiopia, using recurrence quantification analysis", Climate Dynamics, vol. 53, no. 5, 2019, pp. 2557–2572. doi:10.1007/s00382-019-04641-3

rqaci - Confidence Bounds of RQA Measures

Set of routines to estimate the confindence bounds of recurrence-based comlexity measures.

• S. Schinkel, N. Marwan, O. Dimigen, J. Kurths, "Confidence bounds of recurrence-based complexity measures", Physics Letters A, vol. 373, no. 26, 2009, pp. 2245–2250. doi:10.1016/j.physleta.2009.04.045

RSA - Recurrence Structure Analysis.

Time series segmentation technique for the detection of metastable states (aka 'recurrence domains').

• A. Hutt, P. b. Graben, "Sequences by Metastable Attractors: Interweaving Dynamical Systems and Experimental Data", Frontiers in Applied Mathematics and Statistics, vol. 3, 2017, pp. 11. doi:10.3389/fams.2017.00011

SIT - System Identification Tool

System Identification Tool for Matlab.

• A. Sitz, U. Schwarz, J. Kurths, H. U. Voss, "Estimation of parameters and unobserved components for nonlinear systems from noisy time series", Phys. Rev. E, vol. 66, 2002, pp. 016210. doi:10.1103/PhysRevE.66.016210

SOWAS – Wavelet Spectral Analysis and Synthesis

Wavelet and Phase Analysis of bivariate time series.

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

TIGRAMITE - Time series graph based Measures of Information Transfer

Toolbox for estimation couplings.

• J. Runge, J. Heitzig, N. Marwan, J. Kurths, "Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy", Physical Review E, vol. 86, 2012, pp. 061121. doi:10.1103/PhysRevE.86.061121
• J. Runge, J. Heitzig, V. Petoukhov, J. Kurths, "Escaping the Curse of Dimensionality in Estimating Multivariate Transfer Entropy", Phys. Rev. Lett., vol. 108, 2012, pp. 258701.