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The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 129–144 | Cite as

Synchronization processes in complex networks

  • M. Chavez
  • D.-U. Hwang
  • S. BoccalettiEmail author
Article

Abstract.

During the last decades the emergence of collective dynamics in large networks of coupled units has been investigated in fields such as optics, chemistry, biology and ecology. Recently, complex networks have provided a challenging framework for the study of synchronization of dynamical units, based on the interplay between complexity in the overall topology and local dynamical properties of the coupled units. In this work, we review the constructive role played by such complex wirings for the synchronization of networks of coupled dynamical systems. We review the main techniques that have been proposed for assessing the propensity for synchronization (synchronizability) of a given networked system. We will also describe the main applications, especially in the view of selecting the optimal topology in the coupling configuration that provides enhancement of the synchronization features.

Keywords

Lyapunov Exponent Coupling Strength European Physical Journal Special Topic Degree Distribution Random Network 
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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References

  1. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002) Google Scholar
  2. M.E.J. Newman, SIAM Rev. 45, 167 (2003) Google Scholar
  3. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998) Google Scholar
  4. A.L. Barabási, R. Albert, Science 286, 509 (1999) Google Scholar
  5. S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002) Google Scholar
  6. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006) Google Scholar
  7. K. McCann, A. Hastings, G.R. Huxel, Nature 395, 794 (1998) Google Scholar
  8. E.L. Berlow, Nature 398, 330 (1999) Google Scholar
  9. M.E.J. Newman, Phys. Rev. Lett. 89, 208701 (2002) Google Scholar
  10. M.E.J. Newman, Phys. Rev. E 67, 026126 (2003) Google Scholar
  11. G. Buzsáki, C. Geisler, D.A. Henze, X.J. Wang, Trends Neurosci. 27, 186 (2004) Google Scholar
  12. S.H. Strogatz, Nature 410, 268 (2001) Google Scholar
  13. M. Barahona, L.M. Pecora, Phys. Rev. Lett. 89, 054101 (2002) Google Scholar
  14. T. Nishikawa, A.E. Motter, Y.C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91, 014101 (2003) Google Scholar
  15. H. Hong, B.J. Kim, M.Y. Choi, H. Park, Phys. Rev. E 69, 067105 (2004) Google Scholar
  16. A.E. Motter, C.S. Zhou, J. Kurths, Europhys. Lett. 69, 334 (2005) Google Scholar
  17. A.E. Motter, C. Zhou, J. Kurths, Phys. Rev. E 71, 016116 (2005) Google Scholar
  18. D.-U. Hwang, M. Chavez, A. Amann, S. Boccaletti, Phys. Rev. Lett. 94, 138701 (2005) Google Scholar
  19. M. Chavez, D.-U. Hwang, A. Amann, H.G.E. Hentschel, S. Boccaletti, Phys. Rev. Lett. 94, 218701 (2005) Google Scholar
  20. S. Boccaletti, J. Kurths, D.L. Valladares, G. Osipov, C.S. Zhou, Phys. Rep. 366, 1 (2002) Google Scholar
  21. A. Pikovsky, M. Rosemblum, J. Kurths, Synchronization; A Universal Concept in Nonlinear Systems (Cambridge University Press, UK, 2001) Google Scholar
  22. S.C. Manrubia, A.S. Mikhailov, A.H. Zanette, Emergence of Dynamical Order (World Scientific, Singapore, 2004) Google Scholar
  23. L.M. Pecora, T.Ł. Carroll, Phys. Rev. Lett. 80, 2109 (1998) Google Scholar
  24. K.S. Fink, G. Johnson, T. Carroll, D. Mar, L. Pecora, Phys. Rev. E 61, 5080 (2000) Google Scholar
  25. G. Hu, J. Yang, W. Liu, Phys. Rev. E 58, 4440 (1998) Google Scholar
  26. M. Zhan, G. Hu, J. Yang, Phys. Rev. E 62, 2963 (2000) Google Scholar
  27. P. Ashwin, J. Buescu, I. Stewart, Phys. Lett. A 193, 126 (1994) Google Scholar
  28. D.J. Gauthier, J.C. Bienfang, Phys. Rev. Lett. 77, 1751 (1996) Google Scholar
  29. T. Nishikawa, A.E. Motter, Phys. Rev. E 73, 065106(R) (2006) Google Scholar
  30. D.M. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs: Theory and Applications (J. Ambrosius Barth Verlag, Heidelberg, 1995) Google Scholar
  31. F.R.K. Chung, Spectral Graph Theory (Amer. Math. Soc., Providence, RI, 1997) Google Scholar
  32. O.E. Rössler, Phys. Lett. A 57, 397 (1976) Google Scholar
  33. P.M. Gade, C.-K. Hu, Phys. Rev. E 62, 6409 (2000) Google Scholar
  34. Y. Chen, G. Rangarajan, M. Ding, Phys. Rev. E 67, 026209 (2003) Google Scholar
  35. G. Rangarajan, M. Ding, Phys. Lett. A 296, 204 (2002) Google Scholar
  36. X. Li, G. Chen, IEEE Trans. Circuits Syst. I 50, 1381 (2003) Google Scholar
  37. P.G. Lind, J.A.C. Gallas, H.J. Herrmann, Phys. Rev. E 70, 056207 (2004) Google Scholar
  38. W. Lu, T. Chen, Physica D 198, 148 (2004) Google Scholar
  39. A. Stefański, J. Wojewoda, T. Kapitaniak, S. Yanchuk, Phys. Rev. E 70, 026217 (2004) Google Scholar
  40. B. Gong, L. Yang, K. Yang, Phys. Rev. E 72, 037101 (2005) Google Scholar
  41. S.A. Gerschgorin, Izv. Akad. Nauk. USSSR, Otd. Fiz.-Mat. Nauk. 7, 749 (1931) Google Scholar
  42. C.W. Wu, L.O. Chua, IEEE Trans. Circ. Syst.-I 42, 430 (1995) Google Scholar
  43. C.W. Wu, L.O. Chua, IEEE Trans. Circ. Syst.-I 42, 494 (1995) Google Scholar
  44. C.W. Wu, L.O. Chua, IEEE Trans. Circ. Syst.-I 43, 161 (1996) Google Scholar
  45. D.J. Stilwell, E.M. Bollt, D.G. Roberson, SIAM J. Dyn. Sys. 5, 140 (2006) Google Scholar
  46. J.D. Han, N. Bertin, T. Hao, D.S. Goldberg, G.F. Berriz, L.V. Zhang, D. Dupuy, A.J. Walhout, M.E. Cusick, F.P. Roth, M. Vidal, Nature 430, 88 (2004) Google Scholar
  47. A. Destexhe, E. Marder, Nature 431, 789 (2004) Google Scholar
  48. P.W. Anderson, K. Arrow, D. Pines, The Economy as an Evolving Complex System (Addison-Wesley, Redwood City, CA, 1988) Google Scholar
  49. S. Boccaletti, D.-U. Hwang, M. Chavez, A. Amann, J. Kurths, L.M. Pecora, Phys. Rev. E 74, 016102 (2006) Google Scholar
  50. R.E. Amritkar, C.-K. Hu, Chaos 16, 015117 (2006) Google Scholar
  51. X.F. Wang, G. Chen, Int. J. Bifurcat. Chaos 12, 187 (2002) Google Scholar
  52. C.W. Wu, IEEE Trans. Circuits Syst. I 50, 294 (2003) Google Scholar
  53. J.H. Lü, X. Yu, G. Chen, D.Z. Cheng, IEEE Trans. Circuits Syst. I 51, 787 (2004) Google Scholar
  54. J.H. Lü, X. Yu, G. Chen, Physica A 334, 281 (2004) Google Scholar
  55. J.H. Lü, H. Leung, G. Chen, Dynamics of Continuous, Discrete, and Impulsive Systems Series B: Applications, and Algorithms 11, 70 (2004) Google Scholar
  56. J.H. Lü, G.R. Chen, IEEE Trans. Autom. Control 51, 787 (2004) Google Scholar
  57. W. Wang, J.J.E. Slotine, Biol. Cybern. 92, 38 (2005) Google Scholar
  58. V.N. Belykh, I.V. Belykh, M. Hasler, Physica D 195, 159 (2004) Google Scholar
  59. I.V. Belykh, V.N. Belykh, M. Hasler, Physica D 195, 188 (2004) Google Scholar
  60. I. Belykh, E. de Lange, M. Hasler, Phys. Rev. Lett. 94, 188101 (2005) Google Scholar
  61. I. Belykh, M. Hasler, M. Lauret, H. Nijmeijer, Int. J. Bifurcat. Chaos 15, 3423 (2005) Google Scholar
  62. I.V. Belykh, V.N. Belykh, M. Hasler, Physica D 224, 42 (2006) Google Scholar
  63. L. Kocarev, P. Amato, Chaos 15, 02401 (2005) Google Scholar
  64. M. di Bernardo, F. Garofalo, F. Sorrentino (2005) cond-mat/0506236 Google Scholar
  65. M. di Bernardo, F. Garofalo, F. Sorrentino (2005) cond-mat/0504335 Google Scholar
  66. L.M. Pecora, Phys. Rev. E 58, 347 (1998) Google Scholar
  67. Y. Jiang, M. Lozada-Cassou, A. Vinet, Phys. Rev. E 68, 065201 (2003) Google Scholar
  68. C. Zhou, A.E. Motter, J. Kurths, Phys. Rev. Lett. 96, 03101 (2006) Google Scholar
  69. F.M. Atay, T. Biyikoğlu, J. Jost, Physica D 224, 35 (2006) Google Scholar
  70. V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001) Google Scholar
  71. A. Barrat, M. Bartélemy, R. Pastor-Satorras, A. Vespignani, Proc. Natl. Acad. Sci. USA 101, 3747 (2004) Google Scholar
  72. O. Sporns, D.R. Chialvo, M. Kaiser, C.C. Hilgetag, Trends Cogn. Sci. 8, 418 (2004) Google Scholar
  73. S. Song, P.J. Sjöström, M. Reigl, S. Nelson, D.B. Chklovskii, PLoS Biol. 3, e68 (2005) Google Scholar
  74. K.I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001) Google Scholar
  75. S.N. Dorogovtsev, J.F.F. Mendes, Phys. Rev. E 62, 1842 (2000) Google Scholar
  76. J.J. Ramasco, S.N. Dorogovtsev, R. Pastor-Satorras, Phys. Rev. E 70, 036106 (2004) Google Scholar
  77. P. Erdös, A. Rényi, Publ. Math. Debrecen 6, 290 (1959) Google Scholar
  78. P.J. Macdonald, E. Almaas, A.-L. Barabási, Europhys. Lett. 72, 308 (2005) Google Scholar
  79. S. Kirkpatrick, C.D. Gelatt Jr., M.P. Vecchi, Science 220, 671 (1983) Google Scholar
  80. S. Maslov, K. Sneppen, Science 296, 910 (2002) Google Scholar
  81. T. Schreiber, Phys. Rev. Lett. 80, 2105 (1998) Google Scholar
  82. J. Gómez-Gardeñez, Phys. Rev. Lett. 98, 034101 (2007) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.LENA-CNRS UPR-640Paris Cedex 13France
  2. 2.J. Crayton Pruitt Family Department of Biomedical EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.CNR-Istituto dei Sistemi Complessi via Madonna del Piano, 10.50019 Sesto FiorentinoFlorenceItaly

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