A historical review of recurrence plots

Abstract In the last two decades recurrence plots (RPs)were introduced in many different scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and by the study of relationships between RPs and fundamental properties of dynamical systems, this method attracted even more attention. After 20 years of RPs it is time to summarise this development in a historical context.

[1]  P. Mahalanobis.  On the generalized distance in statistics , 1936 .

[2]  Kazuyuki Aihara,et al.  Dynamical Calling Behavior Experimentally Observed in Japanese Tree Frogs (Hyla japonica) , 2007, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[3]  Shirley Dex,et al.  JR 旅客販売総合システム（マルス）における運用及び管理について , 1991 .

[4]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[5]  R Benigni,et al.  Nonlinear methods in the analysis of protein sequences: a case study in rubredoxins. , 2000, Biophysical journal.

[6]  M C Romano,et al.  Distinguishing quasiperiodic dynamics from chaos in short-time series. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Masaru Tomita,et al.  Implications from a Network-Based Topological Analysis of Ubiquitin Unfolding Simulations , 2008, PloS one.

[8]  S. Hermann,et al.  Exploring sitting posture and discomfort using nonlinear analysis methods , 2005, IEEE Transactions on Information Technology in Biomedicine.

[9]  J. Zbilut,et al.  Embeddings and delays as derived from quantification of recurrence plots , 1992 .

[10]  Joseph P. Zbilut,et al.  Characterization of regime shifts in environmental time series with recurrence quantification analysis , 2008 .

[11]  A. Vicino,et al.  Nonlinear time series analysis of dissolved oxygen in the Orbetello Lagoon (Italy) , 2007 .

[12]  J Kurths,et al.  Generating surrogates from recurrences , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  A Giuliani,et al.  Elucidating protein secondary structures using alpha‐carbon recurrence quantifications , 2001, Proteins.

[14]  K. Rypdal,et al.  Experimental evidence of low-dimensional chaotic convection dynamics in a toroidal magnetized plasma. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Catherine Nicolis,et al.  Recurrence time statistics in deterministic and stochastic dynamical systems in continuous time: a comparison , 2000 .

[16]  Procaccia,et al.  First-return maps as a unified renormalization scheme for dynamical systems. , 1987, Physical review. A, General physics.

[17]  Ahmed S. Elwakil,et al.  Mathematical Models of the Twin-T, Wien-bridgeand Family of Minimum Component Electronic ChaosGenerators with Demonstrative Recurrence Plots , 1999 .

[18]  Juergen Kurths,et al.  Generalized Synchronization Indices based on Recurrence in Phase Space , 2004 .

[19]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[20]  C. Sander,et al.  Protein structure comparison by alignment of distance matrices. , 1993, Journal of molecular biology.

[21]  Juergen Kurths,et al.  Detection of synchronization for non-phase-coherent and non-stationary data , 2005 .

[22]  C. Gilmore,et al.  Detecting Linear and Nonlinear Dependence in Stock Returns: New Methods Derived from Chaos Theory , 1996 .

[23]  Alessandro Giuliani,et al.  Recurrence quantification analysis as an empirical test to distinguish relatively short deterministic versus random number series , 2000 .

[24]  Norbert Marwan,et al.  Line structures in recurrence plots , 2005 .

[25]  Jürgen Kurths,et al.  Order patterns recurrence plots in the analysis of ERP data , 2007, Cognitive Neurodynamics.

[26]  J. Kurths,et al.  Testing for nonlinearity in radiocarbon data , 1994 .

[27]  Gustavo K. Rohde,et al.  Stochastic analysis of recurrence plots with applications to the detection of deterministic signals , 2008 .

[28]  Masao Masugi,et al.  Recurrence Plot-Based Approach to the Analysis of IP-Network Traffic in Terms of Assessing Nonstationary Transitions Over Time , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[29]  A. Giuliani,et al.  Detecting deterministic signals in exceptionally noisy environments using cross-recurrence quantification , 1998 .

[30]  Jürgen Kurths,et al.  Characterization of stickiness by means of recurrence. , 2007, Chaos.

[31]  Joseph B. Kruskal,et al.  Time Warps, String Edits, and Macromolecules , 1999 .

[32]  R. Gilmore,et al.  Topological analysis and synthesis of chaotic time series , 1992 .

[33]  Jianbo Gao,et al.  On the structures and quantification of recurrence plots , 2000 .

[34]  Jürgen Kurths,et al.  Estimation of the direction of the coupling by conditional probabilities of recurrence. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  N. Marwan,et al.  Nonlinear analysis of bivariate data with cross recurrence plots , 2002, physics/0201061.

[36]  Grzegorz Litak,et al.  Cycle-to-cycle oscillations of heat release in a spark ignition engine , 2007 .

[37]  L. Thurstone.  A law of comparative judgment. , 1994 .

[38]  Eytan Domany,et al.  Protein folding in contact map space , 2000 .

[39]  David Sankoff,et al.  Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison , 1983 .

[40]  Jürgen Kurths,et al.  How much information is contained in a recurrence plot , 2004 .

[41]  G. McGuire,et al.  Recurrence matrices and the preservation of dynamical properties , 1997 .

[42]  Alfredo Colosimo,et al.  Nonlinear signal analysis methods in the elucidation of protein sequence-structure relationships. , 2002, Chemical reviews.

[43]  Masaru Tomita,et al.  Proteins as networks: usefulness of graph theory in protein science. , 2008, Current protein & peptide science.

[44]  Jürgen Kurths,et al.  Influence of observational noise on the recurrence quantification analysis , 2002 .

[45]  G. Mayer-Kress,et al.  Use of recurrence plots in the analysis of heart beat intervals , 1990, [1990] Proceedings Computers in Cardiology.

[46]  Jin Ningde,et al.  Application of chaotic recurrence plot analysis to identification of oil/water two-phase flow patterns , 2006 .

[47]  N. V. Zolotova,et al.  Phase asynchrony of the north-south sunspot activity , 2006 .

[48]  Jürgen Kurths,et al.  Multivariate recurrence plots , 2004 .

[49]  R. O. Dendy,et al.  Recurrence plot statistics and the effect of embedding , 2005 .

[50]  Philippe Faure,et al.  A new method to estimate the Kolmogorov entropy from recurrence plots: its application to neuronal signals , 1998 .

[51]  H. Kantz,et al.  Curved structures in recurrence plots: the role of the sampling time. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Leonard A. Smith,et al.  Distinguishing between low-dimensional dynamics and randomness in measured time series , 1992 .

[53]  Andreas Groth.  Visualization of coupling in time series by order recurrence plots. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[55]  Peter Hult,et al.  Detection of the 3rdHeart Sound Using Recurrence Time Statistics , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[56]  C L Webber,et al.  Dynamical assessment of physiological systems and states using recurrence plot strategies. , 1994, Journal of applied physiology.

[57]  Nadia Marchettini,et al.  TRANSITION SCENARIOS DURING THE EVOLUTION OF THE BELOUSOV-ZHABOTINSKY REACTION IN AN UNSTIRRED BATCH REACTOR , 1999 .

[58]  A. Giuliani,et al.  Recurrence quantification analysis of the logistic equation with transients , 1996 .

[59]  J. Kurths,et al.  Recurrence-plot-based measures of complexity and their application to heart-rate-variability data. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Sandro Vaienti,et al.  Statistics of Return Times:¶A General Framework and New Applications , 1999 .

[61]  Kazuyuki Aihara,et al.  Determinism Analysis with Iso-Directional Recurrence Plots , 2002 .

[62]  M. Thiel,et al.  Cross recurrence plot based synchronization of time series , 2002, physics/0201062.

[63]  S. Chiba,et al.  Dynamic programming algorithm optimization for spoken word recognition , 1978 .

[64]  J. Kurths,et al.  Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods , 2003, nlin/0303056.

[65]  Shane S. Sturrock,et al.  Time Warps, String Edits, and Macromolecules – The Theory and Practice of Sequence Comparison . David Sankoff and Joseph Kruskal. ISBN 1-57586-217-4. Price £13.95 (US$22·95). , 2000 .

[66]  J. Kurths,et al.  Spurious Structures in Recurrence Plots Induced by Embedding , 2006 .

[67]  J. Kurths,et al.  Analytical Description of Recurrence Plots of White Noise and Chaotic Processes , 2003, nlin/0301027.

[68]  M. Kac.  On the notion of recurrence in discrete stochastic processes , 1947 .

[69]  Julie C. Mitchell,et al.  Singular hydrophobicity patterns and net charge: a mesoscopic principle for protein aggregation/folding , 2004 .

[70]  J. Kurths,et al.  Estimation of dynamical invariants without embedding by recurrence plots. , 2004, Chaos.

[71]  H. Kantz,et al.  Recurrence plot analysis of nonstationary data: the understanding of curved patterns. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[72]  Edward N. Lorenz,et al.  The Mechanics of Vacillation , 1963 .

[73]  Qi-Xiu Li,et al.  Periodicity and Hemispheric Phase Relationship in High-Latitude Solar Activity , 2008 .

[74]  J. Kruskal.  Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[75]  Soo-Yong Kim,et al.  Divergence in perpendicular recurrence plot; quantification of dynamical divergence from short chaotic time series , 1999 .

[76]  Charles L. Webber,et al.  Recurrence Quantification Analysis: Introduction and Historical Context , 2007, Int. J. Bifurc. Chaos.

[77]  P. Ring,et al.  Nonlinear dynamics of giant resonances in atomic nuclei. , 1998, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[78]  Grzegorz Litak,et al.  Analysis of cycle-to-cycle pressure oscillations in a diesel engine , 2008 .

[79]  J Kurths,et al.  Recurrence analysis of strange nonchaotic dynamics. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[80]  Kenneth Ward Church,et al.  Dotplot : a program for exploring self-similarity in millions of lines of text and code , 1993 .

[81]  M. Casdagli.  Recurrence plots revisited , 1997 .

[82]  Jürgen Kurths,et al.  Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm , 2022 .

[83]  G. Krishnan,et al.  DNA sequence analysis: a procedure to find homologies among many sequences , 1986, Nucleic Acids Res..