MENU
  • Scitation Home
SUBMIT YOUR ARTICLE

Thank you

For your interest in the Chaos: An Interdisciplinary Journal of Nonlinear Science

Check for updates on crossmark
Prev Next
No Access Submitted: 11 February 2015 Accepted: 23 March 2015 Published Online: 10 April 2015

Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems

Chaos 25, 097609 (2015); https://doi.org/10.1063/1.4916924
Norbert Marwana) and Jürgen Kurthsb)
more...View Affiliations
ABSTRACT
We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.

ACKNOWLEDGMENTS

We would like to acknowledge support from the IRTG 1740/TRP 2011/50151-0, funded by the DFG/FAPESP, the DFG project “Investigation of past and present climate dynamics and its stability by means of a spatio-temporal analysis of climate data using complex networks” (MA 4759/4-1), and project “Gradual environmental change versus single catastrophe—Identifying drivers of mammalian evolution” (SAW-2013-IZW-2), funded by the Leibniz Association (WGL). Moreover, we thank Niklas Boers for calculations and helpful comments.

REFERENCES

  1. 1. A. H. Monahan, J. C. Fyfe, M. H. P. Ambaum, D. B. Stephenson, and G. R. North, J. Clim. 22, 6501 (2009). https://doi.org/10.1175/2009JCLI3062.1, Google ScholarCrossref
  2. 2. D. Dommenget and M. Latif, J. Clim. 15, 216 (2002). https://doi.org/10.1175/1520-0442(2002)015<0216:ACNOTI>2.0.CO;2, Google ScholarCrossref
  3. 3. S. H. Strogatz, Nature 410, 268 (2001). https://doi.org/10.1038/35065725, Google ScholarCrossref
  4. 4. M. Newman, SIAM Rev. 45, 167 (2003). https://doi.org/10.1137/S003614450342480, Google ScholarCrossref
  5. 5. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D. U. Hwang, Phys. Rep. 424, 175 (2006). https://doi.org/10.1016/j.physrep.2005.10.009, Google ScholarCrossref
  6. 6. L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuño, Proc. Natl. Acad. Sci. U.S.A. 105, 4972 (2008). https://doi.org/10.1073/pnas.0709247105, Google ScholarCrossref
  7. 7. M. Small, in IEEE International Symposium on Circuits and Systems (ISCAS2013) (2013), pp. 2509–2512. Google Scholar
  8. 8. N. Marwan, M. C. Romano, M. Thiel, and J. Kurths, Phys. Rep. 438, 237 (2007). https://doi.org/10.1016/j.physrep.2006.11.001, Google ScholarCrossref
  9. 9. R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, and J. Kurths, Int. J. Bifurcation Chaos 21, 1019 (2011). https://doi.org/10.1142/S0218127411029021, Google ScholarCrossref
  10. 10. J.-P. Eckmann, S. Oliffson Kamphorst, and D. Ruelle, Europhys. Lett. 4, 973 (1987). https://doi.org/10.1209/0295-5075/4/9/004, Google ScholarCrossref
  11. 11. J. P. Zbilut and C. L. Webber, Jr., Phys. Lett. A 171, 199 (1992). https://doi.org/10.1016/0375-9601(92)90426-M, Google ScholarCrossref
  12. 12. N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, and J. Kurths, Phys. Rev. E 66, 026702 (2002). https://doi.org/10.1103/PhysRevE.66.026702, Google ScholarCrossref
  13. 13. N. Marwan, A. Facchini, M. Thiel, J. P. Zbilut, and H. Kantz, Eur. Phys. J. – Spec. Top. 164, 1 (2008). https://doi.org/10.1140/epjst/e2008-00828-2, Google ScholarCrossref
  14. 14. J. S. Iwanski and E. Bradley, Chaos 8, 861 (1998). https://doi.org/10.1063/1.166372, Google ScholarScitation
  15. 15. M. Thiel, M. C. Romano, P. L. Read, and J. Kurths, Chaos 14, 234 (2004). https://doi.org/10.1063/1.1667633, Google ScholarScitation
  16. 16. D. V. Senthilkumar, M. Lakshmanan, and J. Kurths, Chaos 18, 023118 (2008). https://doi.org/10.1063/1.2911541, Google ScholarScitation
  17. 17. E. J. Ngamga, A. Buscarino, M. Frasca, L. Fortuna, A. Prasad, and J. Kurths, Chaos 18, 013128 (2008). https://doi.org/10.1063/1.2897312, Google ScholarScitation
  18. 18. H. Yang and Y. Chen, Chaos 24, 013138 (2014). https://doi.org/10.1063/1.4869306, Google ScholarScitation
  19. 19. M. C. Romano, M. Thiel, J. Kurths, K. Mergenthaler, and R. Engbert, Chaos 19, 015108 (2009). https://doi.org/10.1063/1.3072784, Google ScholarScitation
  20. 20. X. Xu, J. Zhang, and M. Small, Proc. Natl. Acad. Sci. U.S.A. 105, 19601 (2008). https://doi.org/10.1073/pnas.0806082105, Google ScholarCrossref
  21. 21. N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, and J. Kurths, Phys. Lett. A 373, 4246 (2009). https://doi.org/10.1016/j.physleta.2009.09.042, Google ScholarCrossref
  22. 22. F. Strozzi, J.-M. Zaldívar, K. Poljansek, F. Bono, and E. Gutiérrez, “ From complex networks to time series analysis and viceversa: Application to metabolic networks,” Technical Report (EU Joint Research Centre, 2009). Google Scholar
  23. 23. Y. Zou, R. V. Donner, J. F. Donges, N. Marwan, and J. Kurths, Chaos 20, 043130 (2010). https://doi.org/10.1063/1.3523304, Google ScholarScitation
  24. 24. R. V. Donner, J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, Eur. Phys. J. B 84, 653 (2011). https://doi.org/10.1140/epjb/e2011-10899-1, Google ScholarCrossref
  25. 25. C. L. Webber, Jr. and N. Marwan, Recurrence Quantification Analysis – Theory and Best Practices ( Springer, Cham, 2015), p. 421. Google Scholar
  26. 26. O. E. Rössler, Phys. Lett. A 57, 397 (1976). https://doi.org/10.1016/0375-9601(76)90101-8, Google ScholarCrossref
  27. 27. L. L. Trulla, A. Giuliani, J. P. Zbilut, and C. L. Webber, Jr., Phys. Lett. A 223, 255 (1996). https://doi.org/10.1016/S0375-9601(96)00741-4, Google ScholarCrossref
  28. 28. N. Marwan, Int. J. Bifurcation Chaos 21, 1003 (2011). https://doi.org/10.1142/S0218127411029008, Google ScholarCrossref
  29. 29. G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, H. Stepan, J. Kurths, T. Walther, and N. Wessel, Auton. Neurosci. 178, 103 (2013). https://doi.org/10.1016/j.autneu.2013.05.003, Google ScholarCrossref
  30. 30. P. Lang, D.-B. Liu, S.-M. Cai, L. Hong, and P.-L. Zhou, Cell Biochem. Biophys. 66, 331 (2013). https://doi.org/10.1007/s12013-012-9452-0, Google ScholarCrossref
  31. 31. Z. Gao, X. Zhang, N. Jin, R. V. Donner, N. Marwan, and J. Kurths, Europhys. Lett. 103, 50004 (2013). https://doi.org/10.1209/0295-5075/103/50004, Google ScholarCrossref
  32. 32. J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, and J. Kurths, Proc. Natl. Acad. Sci. U.S.A. 108, 20422 (2011). https://doi.org/10.1073/pnas.1117052108, Google ScholarCrossref
  33. 33. D. Eroglu, N. Marwan, S. Prasad, and J. Kurths, Nonlinear Processes Geophys. 21, 1085 (2014). https://doi.org/10.5194/npg-21-1085-2014, Google ScholarCrossref
  34. 34. T. M. Lenton, H. Held, E. Kriegler, J. W. Hall, W. Lucht, S. Rahmstorf, and H. J. Schellnhuber, Proc. Natl. Acad. Sci. U.S.A. 105, 1786 (2008). https://doi.org/10.1073/pnas.0705414105, Google ScholarCrossref
  35. 35. J. Rockstrom, W. Steffen, K. Noone, A. Persson, F. S. Chapin III, E. F. Lambin, T. M. Lenton, M. Scheffer, C. Folke, H. J. Schellnhuber, B. Nykvist, C. A. de Wit, T. Hughes, S. van der Leeuw, H. Rodhe, S. Sorlin, P. K. Snyder, R. Costanza, U. Svedin, M. Falkenmark, L. Karlberg, R. W. Corell, V. J. Fabry, J. Hansen, B. Walker, D. Liverman, K. Richardson, P. Crutzen, and J. A. Foley, Nature 461, 472 (2009). https://doi.org/10.1038/461472a, Google ScholarCrossref
  36. 36. N. Marwan, M. H. Trauth, M. Vuille, and J. Kurths, Climate Dynamics 21, 317 (2003). https://doi.org/10.1007/s00382-003-0335-3, Google ScholarCrossref
  37. 37. T. D. Herbert, L. C. Peterson, K. T. Lawrence, and Z. Liu, Science 328, 1530 (2010). https://doi.org/10.1126/science.1185435, Google ScholarCrossref
  38. 38. D. J. Kennett, S. F. M. Breitenbach, V. V. Aquino, Y. Asmerom, J. Awe, J. U. L. Baldini, P. Bartlein, B. J. Culleton, C. Ebert, C. Jazwa, M. J. Macri, N. Marwan, V. Polyak, K. M. Prufer, H. E. Ridley, H. Sodemann, B. Winterhalder, and G. H. Haug, Science 338, 788 (2012). https://doi.org/10.1126/science.1226299, Google ScholarCrossref
  39. 39. T. D. Herbert, Geochem. Geophys. Geosyst. 2, 1005 (2001). https://doi.org/10.1029/2000GC000055, Google ScholarCrossref
  40. 40. L. Li, Q. Li, J. Tian, P. Wang, H. Wang, and Z. Liu, Earth Planet. Sci. Lett. 309, 10 (2011). https://doi.org/10.1016/j.epsl.2011.04.016, Google ScholarCrossref
  41. 41. T. Blazina, Y. Sun, A. Voegelin, M. Lenz, M. Berg, and L. H. E. Winkel, Nat. Commun. 5, 4717 (2014). https://doi.org/10.1038/ncomms5717, Google ScholarCrossref
  42. 42. J. F. Donges, R. V. Donner, K. Rehfeld, N. Marwan, M. H. Trauth, and J. Kurths, Nonlinear Processes Geophys. 18, 545 (2011). https://doi.org/10.5194/npg-18-545-2011, Google ScholarCrossref
  43. 43. J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, and J. Kurths, Phys. Lett. A 376, 3504 (2012). https://doi.org/10.1016/j.physleta.2012.10.008, Google ScholarCrossref
  44. 44. N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Phys. Rev. Lett. 45, 712 (1980). https://doi.org/10.1103/PhysRevLett.45.712, Google ScholarCrossref
  45. 45. M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Phys. Rev. A 45, 3403 (1992). https://doi.org/10.1103/PhysRevA.45.3403, Google ScholarCrossref
  46. 46. G. H. Haug and R. Tiedemann, Nature 393, 673 (1998). https://doi.org/10.1038/31447, Google ScholarCrossref
  47. 47. M. Medina-Elizalde and D. W. Lea, Science 310, 1009 (2005). https://doi.org/10.1126/science.1115933, Google ScholarCrossref
  48. 48. “ Chinese loess and the east Asian monsoon,” in Late Cenozoic Climate Change in Asia, edited by Z. An ( Springer Netherlands, Dordrecht, 2014). Google ScholarCrossref
  49. 49. C. Karas, D. Nürnberg, A. K. Gupta, R. Tiedemann, K. Mohan, and T. Bickert, Nat. Geosci. 2, 434 (2009). https://doi.org/10.1038/ngeo520, Google ScholarCrossref
  50. 50. Y. Sun, Z. An, S. C. Clemens, J. Bloemendal, and J. Vandenberghe, Earth Planet. Sci. Lett. 297, 525 (2010). https://doi.org/10.1016/j.epsl.2010.07.004, Google ScholarCrossref
  51. 51. A. Tsonis and P. Roebber, Physica A 333, 497 (2004). https://doi.org/10.1016/j.physa.2003.10.045, Google ScholarCrossref
  52. 52. I. Ebert-Uphoff and Y. Deng, Geophys. Res. Lett. 39, L19701, doi: https://doi.org/10.1029/2012GL053269 (2012). Google ScholarCrossref
  53. 53. M. van der Mheen, H. A. Dijkstra, A. Gozolchiani, M. den Toom, Q. Feng, J. Kurths, and E. Hernandez-Garcia, Geophys. Res. Lett. 40, 2714, doi: https://doi.org/10.1002/grl.50515 (2013). Google ScholarCrossref
  54. 54. V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, and J. Kurths, Nonlinear Processes Geophys. 21, 901 (2014). https://doi.org/10.5194/npg-21-901-2014, Google ScholarCrossref
  55. 55. K. Steinhaeuser and N. V. Chawla, Pattern Recognit. Lett. 31, 413 (2010). https://doi.org/10.1016/j.patrec.2009.11.001, Google ScholarCrossref
  56. 56. K. Yamasaki, A. Gozolchiani, and S. Havlin, Phys. Rev. Lett. 100, 228501 (2008). https://doi.org/10.1103/PhysRevLett.100.228501, Google ScholarCrossref
  57. 57. J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, Europhys. Lett. 87, 48007 (2009). https://doi.org/10.1209/0295-5075/87/48007, Google ScholarCrossref
  58. 58. J. I. Deza, C. Masoller, and M. Barreiro, Nonlinear Processes Geophys. 21, 617 (2014). https://doi.org/10.5194/npg-21-617-2014, Google ScholarCrossref
  59. 59. K. Steinhaeuser and A. A. Tsonis, Clim. Dyn. 42, 1665 (2013). https://doi.org/10.1007/s00382-013-1761-5, Google ScholarCrossref
  60. 60. J. H. Feldhoff, S. Lange, J. Volkholz, J. F. Donges, J. Kurths, and F.-W. Gerstengarbe, Clim. Dyn. 44, 1567 (2015). https://doi.org/10.1007/s00382-014-2182-9, Google ScholarCrossref
  61. 61. J. F. Donges, I. Petrova, A. Loew, N. Marwan, and J. Kurths, Clim. Dyn. (published online 2015). https://doi.org/10.1007/s00382-015-2479-3, Google Scholar
  62. 62. J. F. Donges, Y. Zou, N. Marwan, and J. Kurths, Eur. Phys. J. – Spec. Top. 174, 157 (2009). https://doi.org/10.1140/epjst/e2009-01098-2, Google ScholarCrossref
  63. 63. M. Barreiro, A. C. Marti, and C. Masoller, Chaos 21, 013101 (2011). https://doi.org/10.1063/1.3545273, Google ScholarScitation
  64. 64. J. Runge, J. Heitzig, N. Marwan, and J. Kurths, Phys. Rev. E 86, 061121 (2012). https://doi.org/10.1103/PhysRevE.86.061121, Google ScholarCrossref
  65. 65. J. Deza, M. Barreiro, and C. Masoller, Eur. Phys. J. Spec. Top. 222, 511 (2013). https://doi.org/10.1140/epjst/e2013-01856-5, Google ScholarCrossref
  66. 66. J. Hlinka, D. Hartman, M. Vejmelka, J. Runge, N. Marwan, J. Kurths, and M. Paluš, Entropy 15, 2023 (2013). https://doi.org/10.3390/e15062023, Google ScholarCrossref
  67. 67. L. Carpi, P. Saco, O. Rosso, and M. Ravetti, Eur. Phys. J. B 85, 389 (2012). https://doi.org/10.1140/epjb/e2012-30413-7, Google ScholarCrossref
  68. 68. R. Quian Quiroga, T. Kreuz, and P. Grassberger, Phys. Rev. E 66, 041904 (2002). https://doi.org/10.1103/PhysRevE.66.041904, Google ScholarCrossref
  69. 69. N. Malik, N. Marwan, and J. Kurths, Nonlinear Processes Geophys. 17, 371 (2010). https://doi.org/10.5194/npg-17-371-2010, Google ScholarCrossref
  70. 70. N. Boers, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Kurths, and J. A. Marengo, Nat. Commun. 5, 5199 (2014). https://doi.org/10.1038/ncomms6199, Google ScholarCrossref
  71. 71. N. Malik, B. Bookhagen, N. Marwan, and J. Kurths, Clim. Dyn. 39, 971 (2012). https://doi.org/10.1007/s00382-011-1156-4, Google ScholarCrossref
  72. 72. N. Boers, B. Bookhagen, N. Marwan, J. Kurths, and J. Marengo, Geophys. Res. Lett. 40, 4386, doi: https://doi.org/10.1002/grl.50681 (2013). Google ScholarCrossref
  73. 73. J. Zhou and K.-M. Lau, J. Clim. 11, 1020 (1998). https://doi.org/10.1175/1520-0442(1998)011<1020:DAMCEO>2.0.CO;2, Google ScholarCrossref
  74. 74. J. A. Marengo, W. R. Soares, C. Saulo, and M. Nicolini, J. Clim. 17, 2261 (2004). https://doi.org/10.1175/1520-0442(2004)017<2261:COTLJE>2.0.CO;2, Google ScholarCrossref
  75. 75. J. Nogués-Paegle and K. C. Mo, Mon. Weather Rev. 125, 279 (1997). https://doi.org/10.1175/1520-0493(1997)125<0279:AWADCO>2.0.CO;2, Google ScholarCrossref
  76. 76. G. J. Huffman, D. T. Bolvin, E. J. Nelkin, D. B. Wolff, R. F. Adler, G. Gu, Y. Hong, K. P. Bowman, and E. F. Stocker, J. Hydrometeorol. 8, 38 (2007). https://doi.org/10.1175/JHM560.1, Google ScholarCrossref
  1. © 2015 AIP Publishing LLC.

Article Metrics

Views
797
Citations
Crossref 36
Web of Science
ISI 34

Altmetric

Please Note: The number of views represents the full text views from December 2016 to date. Article views prior to December 2016 are not included.

Resources

General Information

 

Website © AIP Publishing LLC. Article copyright remains as specified within the article.
Scitation logo
Lorem ipsum dolor sit amet, consectetur adipiscing elit. Proin imperdiet nibh sed ipsum molestie eu mattis justo malesuada. Curabitur id quam augue, ac eleifend justo. Integer eget metus sagittis velit semper auctor vel et nunc. Phasellus tempus felis at arcu fringilla at ndimentum libero placerat. Aenean ut imperdiet dolor. Nulla pretium mi vestibulum dui dictum sed ullamcorper tellus sodales. Duis non nibh id ipsum feugiat imperdiet id fermentum nunc. Maecenas id ultricies felis. Suspendisse lacinia rhoncus vestibulum. Vestibulum molestie vulputate convallis.Fusce et augue erat, nec mollis mi.