Recurrence-based time series analysis by means of complex network methods

International Journal of Bifurcation and Chaos

Volumn 21, Issue 4, 2011, Pages 1019-1046

  Donner, Reik V ^a,b,c   Small, Michael ^d   Donges, Jonathan F ^b,e   Marwan, Norbert ^b   Zou, Yong ^b   Xiang, Ruoxi ^d   Kurths, Jürgen ^b,e  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b POTSDAM INSTITUTE FOR CLIMATE IMPACT RESEARCH   (Germany)

^c DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^d HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

^e HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Complex networks; recurrence plots; time series analysis

Indexed keywords

COMPLEX NETWORKS; DYNAMICAL SYSTEMS; HARMONIC ANALYSIS; PHASE SPACE METHODS; REAL TIME SYSTEMS;

HIGHER-ORDER; INTERACTING ENTITIES; NETWORK MEASURES; NETWORK-BASED; REAL-WORLD TIME SERIES; RECURRENCE PLOT; STATISTICAL PROPERTIES; STRUCTURAL FEATURE;

TIME SERIES ANALYSIS;

EID: 79959377152     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127411029021     Document Type: Review

References (100)

1. Albert, R. & Barabasi, A. [2002] "Statistical mechanics of complex networks," Rev. Mod. Phys. 74, 47-97.
2. Amaral, L., Scala, A., Barthélémy, M. & Stanley, H. [2000] "Classes of small-world networks," Proc. Nat. Acad. Sci. USA 97, 11149-11152.
3. Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y. & Zhou, C. [2008] "Synchronization in complex networks," Phys. Rep. 469, 93-153.
4. Bandt, C., Groth, A., Marwan, N., Romano, M. C., Thiel, M., Rosenblum, M. & Kurths, J. [2008] "Analysis of bivariate coupling by means of recurrence," Mathematical Methods in Time Series Analysis and Digital Image Processing, eds. Dahlhaus, R., Kurths, J., Maas, P. & Timmer, J., Understanding Complex Systems (Springer, Berlin, Heidelberg), pp. 153-182.
5. Battista, G., Eades, P., Tamassia, R. & Tollis, I. [1994] "Algorithms for drawing graphs: An annotated bibliography," Comput. Geom. Th. Appl. 4, 235-282.
6. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M. & Hwang, D. U. [2006] "Complex networks: Structure and dynamics," Phys. Rep. 424, 175-308. (Pubitemid 43135890)
7. Costa, L. d. F., Rodrigues, F. A., Travieso, G. & Boas, P. R. V. [2007] "Characterization of complex networks: A survey of measurements," Adv. Phys. 56, 167-242. (Pubitemid 46504905)
8. Csárdi, G. & Nepusz, T. [2006] "The igraph software package for complex network research," Int. J. CX.18, 1695.
9. Daw, C., Finney, C. & Tracy, E. [2003] "A review of symbolic analysis of experimental data," Rev. Scient. Instrum. 74, 915-930.
10. de Floriani, L., Marzano, P. & Puppo, E. [1994] "Lineof- sight communication on terrain models," Int. J. Geograph. Inform. Sci. 8, 329-342.
11. Dellnitz, M., von Molo, M. H., Metzner, P., Preis, R. & Schütte, C. [2006] "Graph algorithms for dynamical systems," Analysis, Modeling and Simulation of Multiscale Problems, ed. Mielke, A. (Springer, Heidelberg), pp. 619-646.
12. deMenocal, P. [1995] "Plio-Pleistocene African climate," Science 270, 53-59.
13. Dombrádi, E., Timár, G., Bada, G., Cloetingh, S. & Horváth, F. [2007] "Fractal dimension estimations of drainage network in the Carpathian-Pannonian system," Global and Planetary Change 58, 197-213. (Pubitemid 46921433)
14. Donner, R., Hinrichs, U. & Scholz-Reiter, B. [2008] "Symbolic recurrence plots: A new quantitative framework for performance analysis of manufacturing networks," European Phys. J. - Special Topics 164, 85-104.
15. Donges, J., Zou, Y., Marwan, N. & Kurths, J. [2009a] "The backbone of the climate network," Europhys. Lett. 87, 48007.
16. Donges, J. F., Zou, Y., Marwan, N. & Kurths, J. [2009b] "Complex networks in climate dynamics - Comparing linear and nonlinear network construction methods," European Phys. J. - Special Topics 174, 157-179.
17. Donner, R. V., Zou, Y., Donges, J. F., Marwan, N. & Kurths, J. [2010a] "Ambiguities in recurrence-based complex network representations of time series," Phys. Rev. E 81, 015101(R).
18. Donner, R. V., Zou, Y., Donges, J. F., Marwan, N. & Kurths, J. [2010b] "Recurrence networks - A novel paradigm for nonlinear time series analysis," New J. Phys. 12, 033025.
19. Eckmann, J.-P., Kamphorst, S. O. & Ruelle, D. [1987] "Recurrence plots of dynamical systems," Europhys. Lett. 4, 973-977.
20. Elsner, J. B., Jagger, T. H. & Fogarty, E. A. [2009] "Visibility network of United States hurricanes," Geophys. Res. Lett. 36, L16702.
21. Facchini, A., Mocenni, C., Marwan, N., Vicino, A. & Tiezzi, E. [2007] "Nonlinear time series analysis of dissolved oxygen in the Orbetello Lagoon (Italy)," Ecol. Model. 203, 339-348. (Pubitemid 46529071)
22. Freeman, L. [1979] "Centrality in social networks conceptual clarification," Social Networks 1, 215-239.
23. Gao, J. B. [1999] "Recurrence time statistics for chaotic systems and their applications," Phys. Rev. Lett. 83, 3178-3181. (Pubitemid 129582858)
24. Gao, Z.-Y. & Li, K.-P. [2005] "Evolution of traffic flow with scale-free topology," Chin. Phys. Lett. 22, 2711-2714. (Pubitemid 41379158)
25. Gao, Z.-Y., Li, K.-P., Li, X.-G., Huang, H.-J., Mao, B.-H. & Zheng, J.-F. [2007] "Scaling laws of the network traffic flow," Physica A 380, 577-584. (Pubitemid 46694204)
26. Gao, Z. & Jin, N. [2009a] "Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks," Phys. Rev. E 79, 066303.
27. Gao, Z. & Jin, N. [2009b] "Complex network from time series based on phase space reconstruction," Chaos 19, 033137.
28. Giuliani, A., Benigni, R., Zbilut, J., Webber, C., Sirabella, P. & Colosimo, A. [2002] "Nonlinear signal analysis methods in the elucidation of protein sequence structure relationships," Chem. Rev. 102, 1471-1492.
29. Grassberger, P. & Procaccia, I. [1983] "Measuring the strangeness of strange attractors," Physica D 9, 189-208.
30. Guimera, R., Mossa, S., Turtschi, A. & Amaral, L. [2005] "The worldwide air transportation network: Anomalous centrality, community structure, and cities' global roles," Proc. Nat. Acad. Sci. USA 102, 7794-7799. (Pubitemid 40781017)
31. Horai, S., Yamada, T. & Aihara, K. [2002] "Determinism analysis with iso-directional recurrence plots," IEEJ Trans. Electron. Inform. Syst. 122, 141-147.
32. Kurths, J., Schwarz, U., Sonett, C. P. & Parlitz, U. [1994] "Testing nonlinearity in radiocarbon data," Nonlin. Process. Geophys. 1, 72-75.
33. Lacasa, L., Luque, B., Ballesteros, F., Luque, J. & Nuno, J. C. [2008] "From time series to complex networks: The visibility graph," Proc. Nat. Acad. Sci. USA 105, 4972-4975. (Pubitemid 351738493)
34. Lacasa, L., Luque, B., Luque, J. & Nuno, J. C. [2009] "The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion," Europhys. Lett. 86, 30001.
35. Latora, V. & Marchiori, M. [2001] "Efficient behavior of small-world networks," Phys. Rev. Lett. 87, 198701.
36. Li, K. P. & Gao, Z. Y. [2006] "A topological approach to traffic dynamics," Europhys. Lett. 74, 369-375. (Pubitemid 43600818)
37. Li, P. & Wang, B. [2006] "An approach to Hang Seng index in Hong Kong stock market based on network topological statistics," Chin. Sci. Bull. 51, 624-629. (Pubitemid 44422188)
38. Li, P. & Wang, B.-H. [2007] "Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies," Physica A 378, 519-526. (Pubitemid 46367473)
39. Li, X.-G., Gao, Z.-Y., Li, K.-P. & Zhao, X.-M. [2007] "Relationship between microscopic dynamics in traffic flow and complexity in networks," Phys. Rev. E 76, 016110.
40. Litak, G., Sawicki, J. T. & Kasperek, R. [2009] "Cracked rotor detection by recurrence plots," Nondestructive Testing and Evaluation 24, 347-351.
41. Liu, C. & Zhou, W.-X. [2010] "Superfamily classification of nonstationary time series based on DFA scaling exponents," J. Phys. A 43, 495005.
42. Liu, C., Zhou, W.-X. & Yuan, W.-K. [2010] "Statistical properties of visibility graph of energy dissipation rates in three-dimensional fully developed turbulence," Physica A 389, 2675-2681.
43. Luque, B., Lacasa, L., Ballesteros, F. & Luque, J. [2009] "Horizontal visibility graphs: Exact results for random time series," Phys. Rev. E 80, 046103.
44. Marwan, N., Thiel, M. & Nowaczyk, N. R. [2002a] "Cross recurrence plot based synchronization of time series," Nonlin. Process. Geophys. 9, 325-331. (Pubitemid 34825274)
45. Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A. & Kurths, J. [2002b] "Recurrence plot based measures of complexity and its application to heart rate variability data," Phys. Rev. E 66, 026702.
46. Marwan, N., Trauth, M. H., Vuille, M. & Kurths, J. [2003] "Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods," Clim. Dyn. 21, 317-326. (Pubitemid 37307306)
47. Marwan, N., Kurths, J. & Saparin, P. [2007a] "Generalised recurrence plot analysis for spatial data," Phys. Lett. A 360, 545-551. (Pubitemid 44791765)
48. Marwan, N., Romano, M. C., Thiel, M. & Kurths, J. [2007b] "Recurrence plots for the analysis of complex systems," Phys. Rep. 438, 237-329.
49. Marwan, N., Saparin, P. & Kurths, J. [2007c] "Measures of complexity for 3D image analysis of trabecular bone," European Phys. J. - Special Topics 143, 109-116.
50. Marwan, N. [2008] "A historical review of recurrence plots," European Phys. J. - Special Topics 164, 3-12.
51. Marwan, N., Schinkel, S. & Kurths, J. [2008] "Significance for a recurrence based transition analysis," Proc. 2008 Int. Symp. Nonlinear Theory and Its Applications NOLTA'08, Budapest, Hungary, September 7-10, 2008, pp. 412-415.
52. Marwan, N., Donges, J. F., Zou, Y., Donner, R. V. & Kurths, J. [2009] "Complex network approach for recurrence analysis of time series," Phys. Lett. A 373, 4246-4254.
53. McClymont, E. & Rosell-Melé, A. [2005] "Links between the onset of modern Walker circulation and the mid- Pleistocene climate transition," Geology 33, 389-392. (Pubitemid 40706788)
54. Mudelsee, M. & Raymo, M. [2005] "Slow dynamics of the Northern Hemisphere glaciation," Paleoceanography 20, PA4022.
55. Nawrath, J., Romano, M., Thiel, M., Kiss, I., Wickramasinghe, M., Timmer, J., Kurths, J. & Schelter, B. [2010] "Distinguishing direct from indirect interactions in oscillatory networks with multiple time scales," Phys. Rev. Lett. 104, 038701.
56. Newman, M. [2003] "The structure and function of complex networks," SIAM Rev. 45, 167-256.
57. Ni, X.-H., Jiang, Z.-Q. & Zhou, W.-X. [2009] "Degree distributions of the visibility graphs mapped from fractional brownian motions and multifractal random walks," Phys. Lett. A 373, 3822-3826.
58. Nicolis, G., Garćia Cantú, A. & Nicolis, C. [2005] "Dynamical aspects of interaction networks," Int. J. Bifurcation and Chaos 15, 3467-3480. (Pubitemid 43201367)
59. Packard, N. H., Crutchfield, J. P., Farmer, J. D. & Shaw, R. S. [1980] "Geometry from a time series," Phys. Rev. Lett. 45, 712-716.
60. Padberg, K., Thiere, B., Preis, R. & Dellnitz, M. [2009] "Local expansion concepts for detecting transport barriers in dynamical systems," Commun. Nonlin. Sci. Numer. Simul. 14, 4176-4190.
61. Poincaré, H. [1890] "Sur la problème des trois corps et les équations de la dynamique," Acta Mathematica 13, A3-A270.
62. Procaccia, I., Thomae, S. & Tresser, C. [1987] "Firstreturn maps as a unified renormalization scheme for dynamical systems," Phys. Rev. A 35, 1884-1900.
63. Qian, M.-C., Jiang, Z.-Q. & Zhou, W.-X. [2010] "Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices," J. Phys. A 43, 335002.
64. Ravelo, A., Andreasen, D., Lyle, M., Lyle, A. & Wara, M. [2004] "Regional climate shifts caused by gradual global cooling in the Pliocene epoch," Nature 429, 263-267. (Pubitemid 38684806)
65. Romano, M. C., Thiel, M., Kurths, J. & von Bloh, W. [2004] "Multivariate recurrence plots," Phys. Lett. A 330, 214-223.
66. Romano, M. C., Thiel, M., Kurths, J., Kiss, I. Z. & Hudson, J. [2005] "Detection of synchronization for nonphase- coherent and non-stationary data," Europhys. Lett. 71, 466-472. (Pubitemid 41111354)
67. Romano, M. C., Thiel, M., Kurths, J. & Grebogi, C. [2007] "Estimation of the direction of the coupling by conditional probabilities of recurrence," Phys. Rev. E 76, 036211.
68. Schinkel, S., Dimigen, O. & Marwan, N. [2008] "Selection of recurrence threshold for signal detection," Europ. Phys. J. - Special Topics 164, 45-53.
69. Schinkel, S., Marwan, N., Dimigen, O. & Kurths, J. [2009] "Confidence bounds of recurrence-based complexity measures," Phys. Lett. A 373, 2245-2250.
70. Schirdewan, A., Gapelyuk, A., Fischer, R., Koch, L., Schütt, H., Zacharzowsky, U., Dietz, R., Thierfelder, L. & Wessel, N. [2007] "Cardiac magnetic field map topology quantified by Kullback-Leibler entropy identifies patients with hypertrophic cardiomyopathy," Chaos 17, 015118.
71. Shimada, Y., Kimura, T. & Ikeguchi, T. [2008] "Analysis of chaotic dynamics using measures of the complex network theory," Artificial Neural Networks - ICANN 2008, Pt. I, eds. Kurkova, V., Neruda, R. & Koutnik, J. (Springer, NY), pp. 61-70.
72. Shirazi, A. H., Reza Jafari, G., Davoudi, J., Peinke, J., Tabar, M. R. R. & Sahimi, M. [2009] "Mapping stochastic processes onto complex networks," J. Statist. Mech. Th. Experim. 2009, P07046.
73. Small, M., Yu, D. & Harrison, R. [2001] "Surrogate test for pseudoperiodic time series data," Phys. Rev. Lett. 87, 188101.
74. Small, M., Zhang, J. & Xu, X. [2009] "Transforming time series into complex networks," Complex Sciences. First Int. Conf., Complex 2009. Shanghai, China, February 2009. Revised Papers, Part 2, ed. Zhou, J. (Springer, Berlin), pp. 2078-2089.
75. St. John, K. & Krissek, L. [2002] "The late Miocene to Pleistocene ice-rafting history of southeast Greenland," Boreas 31, 28-35. (Pubitemid 34315979)
76. Takens, F. [1981] "Detecting strange attractors in turbulence," Dynamical Systems and Turbulence, Warwick 1980, eds. Rand, D. & Young, L.-S. (Springer, NY), pp. 366-381.
77. Tang, Q. & Liu, J. [2009] "Network analysis of Shanghai stock exchange composite index and Shenzhen stock exchange component index," Eight Wuhan Int. Conf. E-Business, Vols. I-III, ed. Duserick, F. (Alfred University Press, Alfred), pp. 883-887.
78. Theiler, J. & Rapp, P. [1996] "Re-examination of the evidence for low-dimensional, nonlinear structure in the human electroencephalogram, " Electroencephalogr. Clin. Neurophysiol. 98, 213-222. (Pubitemid 26110265)
79. Thiel, M., Romano, M. C., Read, P. L. & Kurths, J. [2004] "Estimation of dynamical invariants without embedding by recurrence plots," Chaos 14, 234-243. (Pubitemid 38830205)
80. Thiel, M., Romano, M. & Kurths, J. [2006] "Spurious structures in recurrence plots induced by embedding," Nonlin. Dyn. 44.
81. Tiedemann, R., Sarnthein, M. & Shackleton, N. [1994] "Astronomical timescale for the Pliocene Atlantic d18O and dust flux records of Ocean Drilling Program Site 659," Paleoceanography 9, 619-638.
82. Trauth, M., Larrasoana, J. & Mudelsee, M. [2009] "Trends, rhythms and events in Plio-Pleistocene African climate," Quat. Sci. Rev. 28, 399-411.
83. Trulla, L. L., Giuliani, A., Zbilut, J. P. & Webber Jr. C. L. [1996] "Recurrence quantification analysis of the logistic equation with transients," Phys. Lett. A 223, 255-260. (Pubitemid 126392667)
84. Turner, A., Doxa, M., O'Sullivan, D. & Penn, A. [2001] "From isovists to visibility graphs: A methodology for the analysis of architectural space," Environment and Planning B: Planning and Design 28, 103-121. (Pubitemid 32175066)
85. Van Leeuwen, P., Geue, D., Thiel, M., Cysarz, D., Lange, S., Romano, M. C., Wessel, N., Kurths, J. & Grönemeyer, D. H. [2009] "Influence of paced maternal breathing on fetal-maternal heart rate coordination," Proc. Nat. Acad. Sci. USA 106, 13661-13666.
86. Wang, X. & Chen, G. [2002] "Synchronization in smallworld dynamical networks," Int. J. Bifurcation and Chaos 12, 187-192.
87. Webber Jr. C. L., Marwan, N., Facchini, A. & Giuliani, A. [2009] "Simpler methods do it better: Success of recurrence quantification analysis as a general purpose data analysis tool," Phys. Lett. A 373, 3753-3756.
88. Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. [1985] "Determining Lyapunov exponents from a time series," Physica D 16, 285-317.
89. Wu, J., Sun, H. & Gao, Z. [2008] "Mapping to complex networks from chaos time series in the car following model," Traffic and Transportation Studies: Proc. Sixth Int. Conf. Traffic and Transportation Studies, eds.Mao, B., Tian, Z., Huang, H. & Gao, Z. (ASCE & T&DI, Reston, VA), pp. 397-407.
90. Xu, X., Zhang, J. & Small, M. [2008] "Superfamily phenomena and motifs of networks induced from time series," Proc. Nat. Acad. Sci. USA 105, 19601-19605.
91. Yang, Y. & Yang, H. [2008] "Complex network-based time series analysis," Physica A 387, 1381-1386. (Pubitemid 350213269)
92. Yang, Y., Wang, J., Yang, H. & Mang, J. [2009] "Visibility graph approach to exchange rate series," Physica A 388, 4431-4437.
93. Zbilut, J. P. & Webber Jr. C. L. [1992] "Embeddings and delays as derived from quantification of recurrence plots," Phys. Lett. A 171, 199-203.
94. Zbilut, J. P., Mitchell, J. C., Giuliani, A., Marwan, N. & Webber Jr. C. L. [2004] "Singular hydrophobicity patterns and net charge: A mesoscopic principle for protein aggregation/folding," Physica A 343, 348-358.
95. Zhang, J., Luo, X. & Small, M. [2006] "Detecting chaos in pseudoperiodic time series without embedding," Phys. Rev. E 73, 016216.
96. Zhang, J. & Small, M. [2006] "Complex network from pseudoperiodic time series: Topology versus dynamics," Phys. Rev. Lett. 96, 238701.
97. Zhang, J., Sun, J., Luo, X., Zhang, K., Nakamura, T. & Small, M. [2008] "Characterizing pseudoperiodic time series through the complex network approach," Physica D 237, 2856-2865.
98. Zhou, C., Zemanova, L., Zamora, G., Hilgetag, C. C. & Kurths, J. [2006] "Hierarchical organization unveiled by functional connectivity in complex brain networks," Phys. Rev. Lett. 97, 238103.
99. Zhou, C., Zemanova, L., Zamora-Lopez, G., Hilgetag, C. C. & Kurths, J. [2007] "Structure-function relationship in complex brain networks expressed by hierarchical synchronization," New J. Phys. 9, 178.
100. Zou, Y., Donner, R. V., Donges, J. F., Marwan, N. & Kurths, J. [2010] "Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods," Chaos 20, 043130.