The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 85–104 | Cite as

Symbolic recurrence plots: A new quantitative framework for performance analysis of manufacturing networks

  • R. DonnerEmail author
  • U. Hinrichs
  • B. Scholz-Reiter


During the last years, the concept of recurrence plots has received considerable interest as a tool for analysing nonlinear and non-stationary time series. However, in the case of discrete-valued observables or variations on very different time scales, problems may occur in direct interpretations of the results of recurrence quantification analysis (RQA). As a potential solution, we suggest combining this approach with ideas from symbolic time series analysis, which allows an arbitrary static or dynamic coarse-graining of the dynamics that goes beyond recent recurrence plot based methods. As an illustrative application, we discuss how the resulting symbolic recurrence plots may be used for a quantitative investigation of the dynamics of discrete-valued inventory levels of cooperating firms in a manufacturing network. Based on discrete-event simulations, measures from traditional RQA are used to evaluate the performance of the individual firms under different production strategies as well as order policies. The results of our investigations are an important step towards an anticipative knowledge about the performance of manufacturing systems under different conditions, which is of major importance for the planning and control of both production and logistics.


European Physical Journal Special Topic Inventory Level Shannon Entropy Symbolic Sequence Recurrence Plot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. H.D.I. Aberbanel, Analysis of Observed Chaotic Data (Springer, New York, 1996) Google Scholar
  2. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, Cambridge, 1997) Google Scholar
  3. C. Diks, Nonlinear Time Series Analysis – Methods and Applications (World Scientific, Singapore, 1999) Google Scholar
  4. R.V. Donner, S.M. Barbosa (eds.), Nonlinear Time Series Analysis in the Geosciences – Applications in Climatology, Geodynamics, and Solar-Terrestrial Physics (Springer, Berlin, 2008) Google Scholar
  5. C.S. Daw, C.E.A. Finney, E.R. Tracy, Rev. Sci. Instrum. 74, 915 (2003) Google Scholar
  6. J.M. Finn, J.D. Goettee, Z. Toroczkai, M. Anghel, B.P. Wood, Chaos 13, 444 (2003) Google Scholar
  7. J.-P. Eckmann, S.O. Kamphorst, D. Ruelle, Europhys. Lett. 5, 973 (1987) Google Scholar
  8. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007) Google Scholar
  9. C. Rieke, K. Sternickel, R.G. Andrzejak, C.E. Elger, P. David, K. Lehnertz, Phys. Rev. Lett. 88, 244 (2002) Google Scholar
  10. C. Rieke, R.G. Andrzejak, F. Mormann, K. Lehnertz, Phys. Rev. E 69, 046111 (2004) Google Scholar
  11. J.P. Zbilut, C.L. Webber Jr., Phys. Lett. A 171, 199 (1992) Google Scholar
  12. C.L. Webber Jr., J.P. Zbilut, J. Appl. Phys. 76, 965 (1994) Google Scholar
  13. L.L. Trulla, A. Giuliani, J.P. Zbilut, C.L. Webber Jr., Phys. Lett. A 223, 255 (1996) Google Scholar
  14. N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Phys. Rev. E 66, 026702 (2002) Google Scholar
  15. D.B. Vasconcelos, S.R. Lopes, R.L. Viana, J. Kurths, Phys. Rev. E 73, 056207 (2006) Google Scholar
  16. N. Marwan, J. Kurths, P. Saparin, Phys. Lett. A 360, 545 (2007) Google Scholar
  17. A. Groth, Phys. Rev. E 72, 046220 (2005) Google Scholar
  18. A. Groth, Analyse der Wiederkehr in dynamischen Systemen auf einer Ordinalskala, Ph.D. thesis, University of Greifswald, 2006 Google Scholar
  19. N. Marwan, A. Groth, J. Kurths, Chaos Complex. Lett. 2, 301 (2007) Google Scholar
  20. S. Schinkel, N. Marwan, J. Kurths, Cognit. Neurodyn. 1, 317 (2007) Google Scholar
  21. P. Grassberger, H. Kantz, Phys. Lett. A 113, 235 (1985) Google Scholar
  22. F. Christiansen, A. Politi, Nonlinearity 9, 1623 (1996) Google Scholar
  23. F. Christiansen, A. Politi, Physica D 109, 32 (1997) Google Scholar
  24. M.B. Kennel, M. Buhl, Phys. Rev. Lett. 91, 084102 (2003) Google Scholar
  25. Y. Hirata, K. Judd, D. Kilminster, Phys. Rev. E 70, 016215 (2004) Google Scholar
  26. M. Buhl, M.B. Kennel, Phys. Rev. E 71, 046213 (2005) Google Scholar
  27. E.M. Bollt, T. Stanford, Y.-C. Lai, K. Życzkowski, Physica D 154, 259 (2001) Google Scholar
  28. W. Lee, L. Luo, Phys. Rev. E 56, 848 (1997) Google Scholar
  29. W. Li, K. Kaneko, Europhys. Lett. 17, 655 (1992) Google Scholar
  30. C. Bandt, B. Pompe, Phys. Rev. Lett. 88, 174102 (2002) Google Scholar
  31. M. Staniek, K. Lehnertz, Phys. Rev. Lett. 100, 158101 (2008) Google Scholar
  32. C.J. Cellucci, A.M. Albano, P.E. Rapp, Phys. Rev. E 71, 066208 (2003) Google Scholar
  33. W. Ebeling, G. Nicolis, Chaos Solit. Frac. 2, 635 (1992) Google Scholar
  34. M. Thiel, M.C. Romano, J Kurths, Phys. Lett. A 330, 343 (2004) Google Scholar
  35. G. Robinson, M. Thiel [arXiv:0706.4032] [math.DS] (2007) Google Scholar
  36. P. Faure, H. Korn, Physica D 122, 265 (1998) Google Scholar
  37. J.S. Iwanski, E. Bradley, Chaos 8, 861 (1998) Google Scholar
  38. M. Thiel, M.C. Romano, P.L. Read, J. Kurths, Chaos 14, 234 (2004) Google Scholar
  39. C. Letellier, Phys. Rev. Lett. 96, 254102 (2006) Google Scholar
  40. M.C. Romano, M. Thiel, J. Kurths, W. von Bloh, Phys. Lett. A 330, 214 (2004) Google Scholar
  41. J.D. Sterman, Business Dynamics: Systems Thinking and Modelling for a Complex World (McGraw-Hill, Boston, 2000) Google Scholar
  42. W.J. Hopp, M.L. Spearman, Factory Physics (McGraw-Hill, Boston, 2000) Google Scholar
  43. G. Radons, R. Neugebauer (eds.), Nonlinear Dynamics of Production Systems (Wiley Europe, Weinheim, 2004) Google Scholar
  44. C. Daganzo, A Theory of Supply Chains (Springer, Berlin, 2005) Google Scholar
  45. J.W. Forrester, Harvard Business Rev. 36, 37 (1958) Google Scholar
  46. H. Lee, V. Padmanabhan, S. Whang, Sloan Management Rev. 38, 93 (1997) Google Scholar
  47. D. Helbing, New J. Phys. 5, 90 (2003) Google Scholar
  48. D. Helbing, S. Lämmer, U. Witt, T. Brenner, Phys. Rev. E 70, 056118 (2004) Google Scholar
  49. D. Helbing, S. Lämmer, Networks of Interacting Machines: Production Organization in Complex Industrial Systems and Biological Cells, edited by D. Armbruster, A.S. Mikhailov, K. Kaneko (World Scientific, Singapore, 2005), p. 33 Google Scholar
  50. I. Katzorke, A. Pikovsky, Discr. Dyn. Nature Soc. 5, 179 (2000) Google Scholar
  51. H.-P. Wiendahl, J. Worbs, J. Mater. Process. Technol. 139, 28 (2004) Google Scholar
  52. B. Rem, D. Armbruster, Chaos 13, 128 (2003) Google Scholar
  53. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.U. Hwang, Phys. Rep. 424, 175 (2006) Google Scholar
  54. B. Scholz-Reiter, U. Hinrichs, R. Donner, A. Witt, Proc. IASTED Conf. Modelling and Simulation (2006), p. 178 Google Scholar
  55. R. Donner, U. Hinrichs, B. Scholz-Reiter, A. Witt, Proc. NDES 2006 (2006), p. 22 Google Scholar
  56. B. Scholz-Reiter, U. Hinrichs, R. Donner, Proc. CARV 2007 (2007), p. 263 Google Scholar
  57. R. Donner, B. Scholz-Reiter, J. Hinrichs, Manufact. Sci. (in press) Google Scholar
  58. R. Donner, U. Hinrichs, B. Scholz-Reiter, Dynamics in Logistics, edited by H.-D. Haasis, H.-J. Kreowski, B. Scholz-Reiter (Springer, Berlin, 2008), p. 161 Google Scholar
  59. A. Kraskov, H. Stögbauer, P. Grassberger, Phys. Rev. E 69, 066138 (2004) Google Scholar
  60. T. Schreiber, A. Schmitz, Phys. Rev. Lett. 77, 635 (1996) Google Scholar
  61. E.I. Vlahogianni, M.G. Karlaftis, J.C. Golias, Transp. Res. C 14, 351 (2006) Google Scholar
  62. E.I. Vlahogianni, Transp. Res. Board Ann. Meeting 2007, 07-0814 (2007) Google Scholar
  63. E.I. Vlahogianni, C.L. Webber Jr., N. Geroliminis, A. Skabardonis, Transp. Res. C 15, 392 (2007) Google Scholar

Copyright information

© EDP Sciences and Springer 2008

Authors and Affiliations

  1. 1.Institute for Transport and Economics, Dresden University of TechnologyDresdenGermany
  2. 2.BIBA, University of BremenBremenGermany

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