Skip to main content
SpringerLink
Log in

Characterizing Flows by Complex Network Methods

  • Chapter
  • First Online:
Book cover A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 22))

Abstract

During the last years, complex network approaches have demonstrated their great potentials as versatile tools for exploring the structural as well as dynamical properties of complex systems from a variety of different fields. Among others, recent successful examples include their application to studying flow systems in both, abstract mathematical and real-world geophysical contexts. In this context, two recent developments are particularly notable: on the one hand, correlation-based functional network approaches allow inferring statistical interrelationships, for example between macroscopic regions of the Earth’s climate system, which are hidden to more classical statistical analysis techniques. On the other hand, Lagrangian flow networks provide a new tool to identify dynamically relevant structures in atmosphere, ocean or, more generally, the phase space of complex systems. This chapter summarizes these recent developments and provides some illustrative examples highlighting the application of both concepts to selected paradigmatic low-dimensional model systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Newman, M. E. J. (2010). Networks: An introduction. Oxford: Oxford University Press.

    Book  MATH  Google Scholar 

  2. Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., & Hwang, D. U. (2006). Complex networks: Structure and dynamics. Physics Reports, 424, 175–308.

    Article  MathSciNet  MATH  Google Scholar 

  3. Barrat, A., Barthélemy, M., & Vespignani, A. (2008). Dynamical processes on complex networks. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  4. Albert, R., & Barabási, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47–98.

    Article  MathSciNet  MATH  Google Scholar 

  5. Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45, 167–256.

    Article  MathSciNet  MATH  Google Scholar 

  6. da Fontoura Costa, L., Rodrigues, F. A., Travieso, G., & Villas Boas, P. R. (2007). Characterization of complex networks: A survey of measurements. Advances in Physics, 56(1), 167–242.

    Article  Google Scholar 

  7. Fortunato, S. (2010). Community detection in graphs. Physics Reports, 486, 75–174.

    Article  MathSciNet  Google Scholar 

  8. Arenas, A., Diaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008). Synchronization in complex networks. Physics Reports, 469(3), 93–153.

    Article  MathSciNet  Google Scholar 

  9. Rossi, V., Ser-Giacomi, E., López, C., & Hernández-García, E. (2014). Hydrodynamic provinces and oceanic connectivity from a transport network help designing marine reserves. Geophysical Research Letters, 41(8), 2883–2891.

    Article  Google Scholar 

  10. Ser-Giacomi, E., Rossi, V., López, C., & Hernández-García, E. (2015). Flow networks: A characterization of geophysical fluid transport. Chaos, 25, 036404.

    Article  Google Scholar 

  11. Ser-Giacomi, E., Vasile, R., Hernández-García, E., & López, C. (2014). Most probable paths in temporal weighted networks: An application to ocean transport. Physical Review E, 92, 012818.

    Article  Google Scholar 

  12. Ser-Giacomi, E., Vasile, R., Recuerda, I., Hernández-García, E., & López, C. (2015). Dominant transport pathways in an atmospheric blocking event. Chaos, 25(8), 087413.

    Article  MathSciNet  Google Scholar 

  13. Dods, J., Chapman, S. C., & Gjerloev, J. W. (2015). Network analysis of geomagnetic substorms using the SuperMAG database of ground-based magnetometer stations. Journal of Geophysical Research: Space Physics, 120(9), 7774.

    Google Scholar 

  14. Molkenthin, N., Rehfeld, K., Marwan, N., & Kurths, J. (2014). Networks from flows-from dynamics to topology. Scientific Reports, 4, 4119.

    Article  Google Scholar 

  15. Tupikina, L., Molkenthin, N., López, C., Hernández-García, E., Marwan, N., & Kurths, J. (2016). Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics. PLoS One, 11(4), e0153703.

    Article  Google Scholar 

  16. Donges, J. F., Petrova, I., Loew, A., Marwan, N., & Kurths, J. (2015). How complex climate networks complement eigen techniques for the statistical analysis of climatological data. Climate Dynamics, 45(9), 2407–2424.

    Article  Google Scholar 

  17. Zhou, C., Zemanova, L., Zamora, G., Hilgetag, C. C., & Kurths, J. (2006). Hierarchical organization unveiled by functional connectivity in complex brain networks. Physical Review Letters, 97(23), 238103.

    Article  Google Scholar 

  18. 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 Journal of Physics, 9(6), 178.

    Article  Google Scholar 

  19. Tsonis, A., & Roebber, P. (2004). The architecture of the climate network. Physica A, 333, 497–504.

    Article  Google Scholar 

  20. Yamasaki, K., Gozolchiani, A., & Havlin, S. (2008). Climate networks around the globe are significantly affected by El Niño. Physical Review Letters, 100(22), 228501.

    Article  Google Scholar 

  21. Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2009). Complex networks in climate dynamics. European Physical Journal Special Topics, 174(1), 157.

    Article  Google Scholar 

  22. Barreiro, M., Marti, A. C., & Masoller, C. (2011). Inferring long memory processes in the climate network via ordinal pattern analysis. Chaos, 21(1), 013101.

    Article  Google Scholar 

  23. Mantegna, R. N. (1999). Hierarchical structure in financial markets. European Physical Journal B, 11(1), 193.

    Article  Google Scholar 

  24. Onnela, J. P., Kaski, K., & Kertész, J. (2004). Clustering and information in correlation based financial networks. European Physical Journal B, 38(2), 353.

    Article  Google Scholar 

  25. Liu, X. F., & Tse, C. K. (2012). A complex network perspective of world stock markets: synchronization and volatility. International Journal of Bifurcation and Chaos, 22(06), 1250142.

    Article  Google Scholar 

  26. Nicolis, G., García Cantú, A., & Nicolis, C. (2005). Dynamical aspects of interaction networks. International Journal of Bifurcation and Chaos, 15(11), 3467.

    Article  MathSciNet  MATH  Google Scholar 

  27. Sun, X., Small, M., Zhao, Y., & Xue, X. (2014). Characterizing system dynamics with a weighted and directed network constructed from time series data. Chaos, 24(2), 024402.

    Article  MathSciNet  MATH  Google Scholar 

  28. McCullough, M., Small, M., Stemler, T., & Iu, H. H. C. (2015). Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems. Chaos, 25(5), 053101.

    Article  MathSciNet  MATH  Google Scholar 

  29. Donner, R. (2002). Dynamoeffekt in einem niedrig-dimensionalen Modell einer getriebenen Roberts-Strömung. Master’s thesis, University of Potsdam.

    Google Scholar 

  30. Donner, R., Seehafer, N., Sanjuán, M. A., & Feudel, F. (2006). Low-dimensional dynamo modelling and symmetry-breaking bifurcations. Physica D, 223(2), 151.

    Article  MathSciNet  MATH  Google Scholar 

  31. Donner, R., Feudel, F., Seehafer, N., & Sanjuán, M. A. F. (2007). Hierarchical modeling of a forced Roberts dynamo. International Journal of Bifurcation and Chaos, 17(10), 3589.

    Article  MATH  Google Scholar 

  32. Barrat, A., & Weigt, M. (2000). On the properties of small-world network models. European Physical Journal B, 13, 547.

    Article  Google Scholar 

  33. Fagiolo, G. (2007). Clustering in complex directed networks. Physical Review E, 76, 026107.

    Article  Google Scholar 

  34. Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., & Alon, U. (2002). Network motifs: Simple building blocks of complex networks. Science, 298, 824.

    Article  Google Scholar 

  35. Latora, V., & Marchiori, M. (2001). Efficient behavior of small-world networks. Physical Review Letters, 87, 198701.

    Article  Google Scholar 

  36. Donges, J. F., Heitzig, J., Donner, R. V., & Kurths, J. (2012). Analytical framework for recurrence network analysis of time series. Physical Review E, 85, 046105.

    Article  Google Scholar 

  37. Pfeffer, J., & Carley, K. M. (2012). k-Centralities: Local approximations of global measures based on shortest paths. In Proceedings of the 21st International Conference Companion on World Wide Web (pp. 1043–1050). New York: ACM

    Google Scholar 

  38. Ercsey-Ravasz, M., & Toroczkai, Z. (2010). Centrality scaling in large networks. Physical Review Letters, 105(3), 038701.

    Article  Google Scholar 

  39. Ercsey-Ravasz, M., Lichtenwalter, R. N., Chawla, N. V., & Toroczkai, Z. (2012). Range-limited centrality measures in complex networks. Physical Review E, 85(6), 066103.

    Article  Google Scholar 

  40. Lindner, M., & Donner, R. V. (2017). Spatio-temporal organization of dynamics in a two-dimensional periodically driven vortex flow: A Lagrangian flow network perspective. Chaos, 27(3), 035806.

    Article  MathSciNet  Google Scholar 

  41. Barthélemy, M. (2011). Spatial networks. Physics Reports, 499(1), 1.

    Article  MathSciNet  Google Scholar 

  42. Gudmundsson, A., & Mohajeri, N. (2013). Entropy and order in urban street networks. Scientific Reports, 3, 3324.

    Article  Google Scholar 

  43. Mohajeri, N., French, J., & Gudmundsson, A. (2013). Entropy measures of street-network dispersion: Analysis of coastal cities in Brazil and Britain. Entropy, 15(9), 3340.

    Article  MathSciNet  MATH  Google Scholar 

  44. Mohajeri, N., & Gudmundsson, A. (2014). The evolution and complexity of urban street networks. Geographical Analysis, 46(4), 345.

    Article  Google Scholar 

  45. Molkenthin, N., Kutza, H., Tupikina, L., Marwan, N., Donges, J. F., Feudel, U., et al. (2017). Edge anisotropy and the geometric perspective on flow networks. Chaos, 27(3), 035802.

    Article  MathSciNet  Google Scholar 

  46. Heitzig, J., Donges, J. F., Zou, Y., Marwan, N., & Kurths, J. (2012). Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes. European Physical Journal B, 85, 38.

    Article  Google Scholar 

  47. Molkenthin, N., Rehfeld, K., Stolbova, V., Tupikina, L., & Kurths, J. (2014). On the influence of spatial sampling on climate networks. Nonlinear Processes in Geophysics, 21, 651.

    Article  Google Scholar 

  48. Bialonski, S., Horstmann, M. T., & Lehnertz, K. (2010). From brain to earth and climate systems: Small-world interaction networks or not? Chaos, 20(1), 013134.

    Article  MathSciNet  Google Scholar 

  49. Wiedermann, M., Donges, J. F., Kurths, J., & Donner, R. V. (2016). Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes. Physical Review E, 93, 042308.

    Article  Google Scholar 

  50. Dellnitz, M., Hessel-von Molo, M., Metzner, P., Preis, R., & Schütte, C. (2006). Graph algorithms for dynamical systems. In A. Mielke (Ed.) Analysis, modeling and simulation of multiscale problems (pp. 619–645). Heidelberg: Springer.

    Chapter  Google Scholar 

  51. Santitissadeekorn, N., & Bollt, E. (2007). Identifying stochastic basin hopping by partitioning with graph modularity. Physica D, 231(2), 95.

    Article  MathSciNet  MATH  Google Scholar 

  52. Bollt, E.M., & Santitissadeekorn, N. (2013). Applied and computational measurable dynamics. Philadelphia: SIAM

    Book  MATH  Google Scholar 

  53. Froyland, G., & Dellnitz, M. (2003). Detecting and locating near-optimal almost-invariant sets and cycles. SIAM Journal on Scientific Computing, 24(6), 1839.

    Article  MathSciNet  MATH  Google Scholar 

  54. Froyland, G. (2005). Statistically optimal almost-invariant sets. Physica D, 200(3–4), 205.

    Article  MathSciNet  MATH  Google Scholar 

  55. Froyland, G., Padberg, K., England, M. H., & Treguier, A. M. (2007). Detection of coherent oceanic structures via transfer operators. Physical Review Letters, 98(22), 224503.

    Article  Google Scholar 

  56. Dellnitz, M., Froyland, G., Horenkamp, C., Padberg-Gehle, K., & Sen Gupta, A. (2009). Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical investigation based on transfer operators. Nonlinear Processes in Geophysics, 16(6), 655.

    Article  Google Scholar 

  57. Froyland, G., Santitissadeekorn, N., & Monahan, A. (2010). Transport in time-dependent dynamical systems: Finite-time coherent sets. Chaos, 20(4), 043116.

    Article  MathSciNet  MATH  Google Scholar 

  58. Santitissadeekorn, N., Froyland, G., & Monahan, A. (2010). Optimally coherent sets in geophysical flows: A transfer-operator approach to delimiting the stratospheric polar vortex. Physical Review E, 82(5), 056311.

    Article  Google Scholar 

  59. Froyland, G., Horenkamp, C., Rossi, V., Santitissadeekorn, N. & Gupta, A. S. (2012). Three-dimensional characterization and tracking of an Agulhas Ring. Ocean Modelling, 52, 69.

    Article  Google Scholar 

  60. Banisch, R., & Koltai, P. (2017). Understanding the geometry of transport: Diffusion maps for Lagrangian trajectory data unravel coherent sets. Chaos, 27(3), 035804.

    Article  MathSciNet  MATH  Google Scholar 

  61. Lindner, M., & Hellmann, F. (2018). Stochastic basins of attraction and generalized committor functions. Preprint. arXiv:1803.06372.

    Google Scholar 

  62. Jacobi, M. N., André, C., Döös, K., & Jonsson, P. R. (2012). Identification of subpopulations from connectivity matrices. Ecography, 35(11), 1004.

    Article  Google Scholar 

  63. Froyland, G. (2005). Statistically optimal almost-invariant sets. Physica D, 200(3–4), 205.

    Article  MathSciNet  MATH  Google Scholar 

  64. Froyland, G., & Padberg, K. (2009). Almost-invariant sets and invariant manifolds-connecting probabilistic and geometric descriptions of coherent structures in flows. Physica D, 238(16), 1507.

    Article  MathSciNet  MATH  Google Scholar 

  65. Froyland, G. 2001. Extracting dynamical behavior via Markov models. In Nonlinear dynamics and statistics (pp. 281–321). Berlin: Springer

    Chapter  Google Scholar 

  66. Klus, S., Koltai, P., & Schütte, C. (2016). On the numerical approximation of the Perron-Frobenius and Koopman operator. Journal of Computational Dynamics, 3(1), 51–79.

    MathSciNet  MATH  Google Scholar 

  67. Froyland, G., Junge, O., & Koltai, P. (2013). Estimating long-term behavior of flows without trajectory integration: the infinitesimal generator approach. SIAM Journal on Numerical Analysis, 51(1), 223–247

    Article  MathSciNet  MATH  Google Scholar 

  68. Cencini, M., Lacorata, G., Vulpiani, A., & Zambianchi, E. (1999). Mixing in a meandering jet: a Markovian approximation. Journal of Physical Oceanography, 29(10), 2578.

    Article  Google Scholar 

  69. Bower, A. S. (1991). A simple kinematic mechanism for mixing fluid parcels across a meandering jet. Journal of Physical Oceanography, 21(1), 173.

    Article  Google Scholar 

  70. Samelson, R. M. (1992). Fluid exchange across a meandering jet. Journal of Physical Oceanography, 22, 431.

    Article  Google Scholar 

  71. Raynal, F., & Wiggins, S. (2006). Lobe dynamics in a kinematic model of a meandering jet. I. Geometry and statistics of transport and lobe dynamics with accelerated convergence. Physica D, 223(1), 7.

    Article  MathSciNet  MATH  Google Scholar 

  72. Peikert, R., Pobitzer, A., Sadlo, F., & Schindler, B. (2014). A Comparison of Finite-Time and Finite-Size Lyapunov Exponents (pp. 187–200). Cham: Springer International Publishing.

    MATH  Google Scholar 

  73. Shadden, S. C., Lekien, F., & Marsden, J. E. (2005). Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows. Physica D, 212(3–4), 271.

    Article  MathSciNet  MATH  Google Scholar 

  74. Rodríguez-Méndez, V., Ser-Giacomi, E., & Hernández-García, E. (2017). Clustering coefficient and periodic orbits in flow networks. Chaos, 27(3), 035803.

    Article  MathSciNet  Google Scholar 

  75. Tabeling, P., Perrin, B., & Fauve, S. (1987). Instability of a linear array of forced vortices. Europhysics Letters, 3(4), 459.

    Article  Google Scholar 

  76. Tabeling, P., Cardoso, O., & Perrin, B. (1990). Chaos in a linear array of vortices. Journal of Fluid Mechanics, 213, 511.

    Article  Google Scholar 

  77. Witt, A., Braun, R., Feudel, F., Grebogi, C., & Kurths, J. (1999). Tracer dynamics in a flow of driven vortices. Physical Review E, 59(2), 1605.

    Article  MathSciNet  Google Scholar 

  78. Feudel, F., Witt, A., Gellert, M., Kurths, J., Grebogi, C., & Sanjuán, M. (2005). Intersections of stable and unstable manifolds: The skeleton of Lagrangian chaos. Chaos, Solitons and Fractals, 24(4), 947.

    Article  MathSciNet  MATH  Google Scholar 

  79. Hadjighasem, A., Karrasch, D., Teramoto, H., & Haller, G. (2016). Spectral-clustering approach to Lagrangian vortex detection. Physical Review E, 93, 063107.

    Article  Google Scholar 

  80. Padberg-Gehle, K., & Schneide, C. (2017). Network-based study of Lagrangian transport and mixing. Nonlinear Processes in Geophysics, 24(4), 661.

    Article  Google Scholar 

  81. Froyland, G. (2013). An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems. Physica D, 250, 1.

    Article  MathSciNet  MATH  Google Scholar 

  82. Froyland, G., Stuart, R. M., & van Sebille, E. (2014). How well-connected is the surface of the global ocean? Chaos, 24(3), 033126.

    Article  MathSciNet  MATH  Google Scholar 

  83. Van Sebille, E., England, M. H., & Froyland, G. (2012). Origin, dynamics and evolution of ocean garbage patches from observed surface drifters. Environmental Research Letters, 7(4), 044040.

    Article  Google Scholar 

  84. Froyland, G., & Padberg-Gehle, K. (2012). Finite-time entropy: A probabilistic approach for measuring nonlinear stretching. Physica D, 241(19), 1612.

    Article  MATH  Google Scholar 

  85. Fujiwara, N., Kirchen, K., Donges, J. F., & Donner, R. V. (2017). A perturbation-theoretic approach to Lagrangian flow networks. Chaos, 27(3), 035813.

    Article  MathSciNet  MATH  Google Scholar 

  86. Rheinwalt, A., Marwan, N., Kurths, J., Werner, P. C., & Gerstengarbe, F. W. (2012). Boundary effects in network measures of spatially embedded networks. Europhysics Letters, 100(2), 28002.

    Article  Google Scholar 

  87. Rehfeld, K., Marwan, N., Breitenbach, S. F. M., & Kurths, J. (2013). Late Holocene Asian summer monsoon dynamics from small but complex networks of paleoclimate data. Climate Dynamics, 41(1), 3.

    Article  Google Scholar 

  88. Gelbrecht, M., Boers, N., & Kurths, J. (2017). A complex network representation of wind flows. Chaos, 27, 035808.

    Article  Google Scholar 

  89. Van Der Mheen, M., Dijkstra, H.A., Gozolchiani, A., Den Toom, M., Feng, Q., Kurths, J., et al. (2013). Interaction network based early warning indicators for the Atlantic MOC collapse. Geophysical Research Letters, 40(11), 2714.

    Article  Google Scholar 

  90. Tirabassi, G., Viebahn, J., Dakos, V., Dijkstra, H., Masoller, C., Rietkerk, M., et al. (2014). Interaction network based early-warning indicators of vegetation transitions. Ecological Complexity, 19, 148.

    Article  Google Scholar 

  91. Feng, Q. Y., Viebahn, J. P., & Dijkstra, H. A. (2014). Deep ocean early warning signals of an Atlantic MOC collapse. Geophysical Research Letters, 41(16), 6009.

    Article  Google Scholar 

  92. Rodríguez-Méndez, V., Eguíluz, V. M., Hernández-García, E., & Ramasco, J. J. (2016). Percolation-based precursors of transitions in extended systems. Scientific Reports, 6, 29552.

    Article  Google Scholar 

  93. Tsonis, A., & Swanson, K. (2008). Topology and predictability of El Niño and La Niña networks. Physical Review Letters, 100(22), 1.

    Article  Google Scholar 

  94. Gozolchiani, A., Yamasaki, K., Gazit, O. & Havlin, S. (2008). Pattern of climate network blinking links follows El Niño events. Europhysics Letters, 83(2), 28005.

    Article  Google Scholar 

  95. Martin, E., Paczuski, M., & Davidsen, J. (2013). Interpretation of link fluctuations in climate networks during El Niño periods. Europhysics Letters, 102(4), 48003.

    Article  Google Scholar 

  96. Radebach, A., Donner, R. V., Runge, J., Donges, J. F., & Kurths, J. (2013). Disentangling different types of El Niño episodes by evolving climate network analysis. Physical Review E, 88(5), 052807.

    Article  Google Scholar 

  97. Wiedermann, M., Radebach, A., Donges, J. F., Kurths, J., & Donner, R. V. (2016). A climate network-based index to discriminate different types of El Niño and La Niña. Geophysical Research Letters, 43(13), 7176.

    Article  Google Scholar 

  98. Ludescher, J., Gozolchiani, A., Bogachev, M. I., Bunde, A., Havlin, S., & Schellnhuber, H. J. (2013). Improved El Niño forecasting by cooperativity detection. Proceedings of the National Academy of Sciences, 110(29), 11742.

    Article  Google Scholar 

  99. Ludescher, J., Gozolchiani, A., Bogachev, M. I., Bunde, A., Havlin, S., & Schellnhuber, H. J. (2014). Very early warning of next El Niño. Proceedings of the National Academy of Sciences, 111(6), 2064.

    Google Scholar 

  100. Quian Quiroga, R., Kreuz, T., & Grassberger, P. (2002). Event synchronization: A simple and fast method to measure synchronicity and time delay patterns. Physical Review E, 66, 041904.

    Article  MathSciNet  Google Scholar 

  101. Malik, N., Marwan, N., & Kurths, J. (2010). Spatial structures and directionalities in Monsoonal precipitation over South Asia. Nonlinear Processes in Geophysics, 17(5), 371.

    Article  Google Scholar 

  102. Malik, N., Bookhagen, B., Marwan, N., & Kurths, J. (2011). Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks. Climate Dynamics, 39(3–4), 971.

    Google Scholar 

  103. Stolbova, V., Martin, P., Bookhagen, B., Marwan, N., & Kurths, J. (2014). Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka. Nonlinear Processes in Geophysics, 21(4), 901.

    Article  Google Scholar 

  104. Boers, N., Bookhagen, B., Marwan, N., Kurths, J., & Marengo, J. (2013). Complex networks identify spatial patterns of extreme rainfall events of the South American Monsoon System. Geophysical Research Letters, 40(16), 4386.

    Article  Google Scholar 

  105. Boers, N., Bookhagen, B., Barbosa, H. M. J., Marwan, N., Kurths, J., & Marengo, J. A. (2014). Prediction of extreme floods in the eastern Central Andes based on a complex networks approach. Nature Communications, 5, 5199.

    Article  Google Scholar 

  106. Pöschke, P., Sokolov, I. M., Nepomnyashchy, A. A., & Zaks, M. A. (2016). Anomalous transport in cellular flows: The role of initial conditions and aging. Physical Review E, 94, 032128.

    Article  Google Scholar 

Download references

Acknowledgements

This work has been financially supported by the BMBF Young Investigator’s Group CoSy-CC2 (grant no. 01LN1306A) and the International Research Training Group IRTG 1740/TRP 2014/50151-0, jointly funded by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) and the São Paulo Research Foundation (FAPESP, Fundação de Amparo à Pesquisa do Estado de São Paulo).

Author information

Authors and Affiliations

  1. Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Reik V. Donner

  2. Potsdam Institute for Climate Impact Research, Potsdam, Germany

    Michael Lindner

  3. Department of Mathematics, Humboldt University, Berlin, Germany

    Michael Lindner

  4. Laboratoire de Physique de la Matiere Condensee, Ecole Polytechnique, Palaiseau, France

    Liubov Tupikina

  5. Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

    Nora Molkenthin

Authors
  1. Reik V. Donner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Lindner
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liubov Tupikina
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Nora Molkenthin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Reik V. Donner .

Editor information

Editors and Affiliations

  1. Instituto Nacional de Pesquisas Espaciais – INPE, São José dos Campos, Brazil

    Elbert E. N. Macau

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Donner, R.V., Lindner, M., Tupikina, L., Molkenthin, N. (2019). Characterizing Flows by Complex Network Methods. In: Macau, E. (eds) A Mathematical Modeling Approach from Nonlinear Dynamics to Complex Systems . Nonlinear Systems and Complexity, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-78512-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-78512-7_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78511-0

  • Online ISBN: 978-3-319-78512-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation