Computational Complexity

2012 Edition
| Editors: Robert A. Meyers (Editor-in-Chief)

Synchronization Phenomena on Networks

  • Guanrong Chen
  • Ming Zhao
  • Tao Zhou
  • Bing-Hong Wang
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-1800-9_196

Article Outline

Glossary

Definition of the Subject

Introduction

Basic Concepts of Network Synchronization

Synchronizability Versus Structure

Enhancing Network Synchronizability

Future Research Outlook

Acknowledgments

Bibliography

Keywords

Manifold Coherence Sine Huygens 
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Notes

Acknowledgments

The authors thank the American Physics Society and the Elsevier Publisher for their permission to use some of their publishedsimulation figures, which have all been referenced (in the figure captions). The authors also thank Dr. Jian-Guo Liu for his helpful commentsand suggestions. G.R.C. was supported by the NSFC/RGC joint research scheme under grant N‑CityU107/07.B.H.W. was supported by the NNSFCunder Grants 10472116 and A0524701, and the Specialized Program under the Presidential Funds of CAS. T.Z. was supported by NNSFC under Grants10635040 and 70471033.

Bibliography

  1. 1.
    Albert R, Barabási AL (2002) Rev Mod Phys 74:47Google Scholar
  2. 2.
    Dorogovtsev SN, Mendes JFF (2002) Adv Phys 51:1079CrossRefGoogle Scholar
  3. 3.
    Newman MEJ (2003) SIAM Rev 45:167MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Boccaletti S, Latora V, Moreno Y, Chaves M, Hwang DU (2006) Phys Rep424:175MathSciNetCrossRefGoogle Scholar
  5. 5.
    da F Costa L, Rodrigues FA, Travieso G, Boas PRV (2007) Adv Phys56:167CrossRefGoogle Scholar
  6. 6.
    Pastor-Satorras R, Vespignani A (2001) Phys Rev Lett86:3200CrossRefGoogle Scholar
  7. 7.
    Zhu CP, Xiong SJ, Tian YJ, Li N, Jiang KS (2004) Phys Rev Lett92:218702CrossRefGoogle Scholar
  8. 8.
    Zhou T, Yan G, Wang BH (2005) Phys Rev E 71:046141CrossRefGoogle Scholar
  9. 9.
    Zhou T, Fu ZQ, Wang BH (2006) Prog Nat Sci 16:452MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Zhou T, Liu JG, Bai WJ, Chen GR, Wang BH (2006) Phys Rev E74:056109CrossRefGoogle Scholar
  11. 11.
    Motter AE, Lai YC (2002) Phys Rev E 66:065102CrossRefGoogle Scholar
  12. 12.
    Goh KI, Lee DS, Kahng B, Kim D (2003) Phys Rev Lett91:148701CrossRefGoogle Scholar
  13. 13.
    Motter AE (2004) Phys Rev Lett 93:098701CrossRefGoogle Scholar
  14. 14.
    Zhou T, Wang BH (2005) Chin Phys Lett 22:1072CrossRefGoogle Scholar
  15. 15.
    Galstyan A, Cohen P (2007) Phys Rev E 75:036109CrossRefGoogle Scholar
  16. 16.
    Guimerá R, Díaz-Guilera A, Vega-Redondo F, Cabrales A, Arenas A (2002) PhysRev Lett 89:248701Google Scholar
  17. 17.
    Tadić B, Thurner S, Rodgers GJ (2004) Phys Rev E69:036102Google Scholar
  18. 18.
    Zhao L, Lai YC, Park K, Ye N (2005) Phys Rev E71:026125CrossRefGoogle Scholar
  19. 19.
    Yan G, Zhou T, Hu B, Fu ZQ, Wang BH (2006) Phys Rev E73:046108CrossRefGoogle Scholar
  20. 20.
    Wang BH, Zhou T (2007) J Korean Phys Soc 50:134CrossRefGoogle Scholar
  21. 21.
    Watts DJ, Strogatz SH (1998) Nature 393:440CrossRefGoogle Scholar
  22. 22.
    Barabási AL, Albert R (1999) Science 286:509Google Scholar
  23. 23.
    Strogatz SH, Stewart I (1993) Sci Am 269:102CrossRefGoogle Scholar
  24. 24.
    Gray CM (1994) J Comput Neurosci 1:11CrossRefGoogle Scholar
  25. 25.
    Néda Z, Ravasz E, Vicsek T, Barabási AL (2000) Phys Rev E61:6987Google Scholar
  26. 26.
    Glass L (2001) Nature 410:277CrossRefGoogle Scholar
  27. 27.
    Chen G, Dong X (1998) From Chaos Order.World Scientific,SingaporeMATHGoogle Scholar
  28. 28.
    Erdös P, Rényi A (1960) Pub Math Ins Hung Acad Sci5:17Google Scholar
  29. 29.
    Wang XF (2002) Int J Bifurc Chaos 12:885MATHCrossRefGoogle Scholar
  30. 30.
    Heidelberger R (2007) Nature 450:625CrossRefGoogle Scholar
  31. 31.
    Heagy JF, Carroll TL, Pecora LM (1994) Phys Rev E50:1874CrossRefGoogle Scholar
  32. 32.
    Stefański A, Perlikowski P, Kapitaniak T (2007) Phys Rev E75:016210Google Scholar
  33. 33.
    Wu CW, Chua LO (1995) IEEE Trans Circuits Syst I42:430MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Jost J, Joy MP (2001) Phys Rev E 65:016201MathSciNetCrossRefGoogle Scholar
  35. 35.
    Gade PM (1996) Phys Rev E 54:64CrossRefGoogle Scholar
  36. 36.
    Manrubia SC, Mikhailov AS (1999) Phys Rev E60:1579CrossRefGoogle Scholar
  37. 37.
    Gade PM, Hu CK (1999) Phys Rev E 60:4966CrossRefGoogle Scholar
  38. 38.
    Gade PM, Hu CK (2000) Phys Rev E 62:6409CrossRefGoogle Scholar
  39. 39.
    Lago-Fernández LF, Huerta R, Corbacho F, Sigüenza JA (2000) Phys Rev Lett84:2758Google Scholar
  40. 40.
    Wang XF, Chen G (2002) Int J Bifurc Chaos Appl Sci Eng12:187CrossRefGoogle Scholar
  41. 41.
    Wang XF, Chen G (2002) IEEE Trans Circuits Syst I49:54CrossRefGoogle Scholar
  42. 42.
    Barahona M, Pecora LM (2002) Phys Rev Lett89:054101CrossRefGoogle Scholar
  43. 43.
    Jiang PQ, Wang BH, Bu SL, Xia QH, Luo XS (2004) Int J Mod Phys B18:2674MATHCrossRefGoogle Scholar
  44. 44.
    Lind PG, Gallas JAC, Herrmann HJ (2004) Phys Rev E70:056207CrossRefGoogle Scholar
  45. 45.
    Pecora LM, Carrol TL (1998) Phys Rev Lett 80:2109CrossRefGoogle Scholar
  46. 46.
    Hu G, Yang J, Liu W (1998) Phys Rev E 58:4440CrossRefGoogle Scholar
  47. 47.
    Pecora LM, Barahona M (2005) Chaos Complex Lett1:61MATHGoogle Scholar
  48. 48.
    Nishikawa T, Motter AE (2006) Phys Rev E73:065106CrossRefGoogle Scholar
  49. 49.
    Kuramoto Y (1975) In: Araki H (ed) Internaltional Symposium on MathematicalProblems in Theoretical Physics. Lecture Notes in Physics, vol 30.Springer, New YorkGoogle Scholar
  50. 50.
    Kuramoto Y (1984) Chemical Oscillations, Wave and Turbulence.Springer,BerlinCrossRefGoogle Scholar
  51. 51.
    Kuramoto Y, Nishikawa I (1987) J Stat Phys 49:569MathSciNetMATHCrossRefGoogle Scholar
  52. 52.
    Pikovsky A (2001) Synchronization.Cambridge University Press,CambridgeMATHCrossRefGoogle Scholar
  53. 53.
    Acebrón JA, Bonilla LL, Vicente CJP, Ritort F, Spigler R (2005) Rev Mod Phys77:137Google Scholar
  54. 54.
    Nishikawa T, Motter AE, Lai YC, Hoppensteadt FC (2003) Phys Rev Lett91:014101CrossRefGoogle Scholar
  55. 55.
    Newman MEJ, Strogatz SH, Watts DJ (2001) Phys Rev E64:026118CrossRefGoogle Scholar
  56. 56.
    Dorogovtsev SN, Mendes JFF (2000) Phys Rev E62:1842CrossRefGoogle Scholar
  57. 57.
    Hong H, Kim BJ, Choi MY, Park H (2004) Phys Rev E69:067105CrossRefGoogle Scholar
  58. 58.
    Freeman L (1979) Soc Netw 1:215CrossRefGoogle Scholar
  59. 59.
    Newman MEJ (2001) Phys Rev E 64:016132CrossRefGoogle Scholar
  60. 60.
    Zhou T, Liu JG, Wang BH (2006) Chin Phys Lett23:2327CrossRefGoogle Scholar
  61. 61.
    Fan ZP (2006) Complex Networks: From Topology to Dynamics. Ph D Thesis, CityUniversity of Hong KongGoogle Scholar
  62. 62.
    Zhao M, Zhou T, Wang BH, Yan G, Yang HJ, Bai WJ (2006) Physica A371:773CrossRefGoogle Scholar
  63. 63.
    Maslv S, Sneppen K (2002) Science 296:910CrossRefGoogle Scholar
  64. 64.
    Kim BJ (2004) Phys Rev E 69:045101(R)Google Scholar
  65. 65.
    McGraw PN, Menzinger M (2005) Phys Rev E72:015101MathSciNetCrossRefGoogle Scholar
  66. 66.
    Gómez-Gardeñes J, Moreno Y, Arenas A (2007) Phys Rev Lett98:034101Google Scholar
  67. 67.
    Wu X, Wang BH, Zhou T, Wang WX, Zhao M, Yang HJ (2006) Chin Phys Lett23:1046CrossRefGoogle Scholar
  68. 68.
    Holme P, Kim BJ (2002) Phys Rev E 65: 026107CrossRefGoogle Scholar
  69. 69.
    Newman MEJ (2002) Phys Rev Lett 89:208701CrossRefGoogle Scholar
  70. 70.
    di Bernardo M, Garofalo F, Sorrentino F (2007) Int J Bifurc Chaos 17:3499MathSciNetCrossRefGoogle Scholar
  71. 71.
    Sorrentino F, di Bernardo M, Cuéllar GH, Boccaletti S (2006) Physica D224:123Google Scholar
  72. 72.
    Chavez M, Hwang DU, Martinerie J, Boccaletti S (2006) Phys Rev E74:066107MathSciNetCrossRefGoogle Scholar
  73. 73.
    Zhao M, Zhou T, Wang BH, Ou Q, Ren J (2006) Eru Phys J B53:375CrossRefGoogle Scholar
  74. 74.
    Huang L, Park K, Lai YC, Yang L, Yang K (2006) Phys Rev Lett97:164101CrossRefGoogle Scholar
  75. 75.
    Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D (2004) Proc Natl AcadSci USA 101:2658CrossRefGoogle Scholar
  76. 76.
    Zhou T, Zhao M, Chen G, Yan G, Wang BH (2007) Phys Lett A368:431CrossRefGoogle Scholar
  77. 77.
    Donetti L, Hurtado PI, Muñoz MA (2005) Phys Rev Lett95:188701Google Scholar
  78. 78.
    Motter AE, Zhou C, Kurths J (2005) Phys Rev E71:016116CrossRefGoogle Scholar
  79. 79.
    Motter AE, Zhou C, Kurths J (2005) Europhys Lett69:334CrossRefGoogle Scholar
  80. 80.
    Motter AE, Zhou C, Kurths J (2005) AIP Conf Proc776:201MathSciNetCrossRefGoogle Scholar
  81. 81.
    Hwang DU, Chavez M, Amann A, Boccaletti S (2005) Phys Rev Lett94:138701CrossRefGoogle Scholar
  82. 82.
    Dorogovtsev SN, Mendes JFF, Samukhin AN (2000) Phys Rev Lett85:4633CrossRefGoogle Scholar
  83. 83.
    Krapivsky PL, Redner S (2001) Phys Rev E63:066123CrossRefGoogle Scholar
  84. 84.
    Zou Y, Zhu J, Chen G (2006) Phys Rev E 74:046107CrossRefGoogle Scholar
  85. 85.
    Chavez M, Hwang DU, Amann A, Hentschel HGE, Boccaletti S (2005) Phys Rev Lett94:218701CrossRefGoogle Scholar
  86. 86.
    Chavez M, Hwang DU, Amann A, Boccaletti S (2006) Chaos16:015106MathSciNetCrossRefGoogle Scholar
  87. 87.
    Goh KI, Kahng B, Kim D (2001) Phys Rev Lett87:278701CrossRefGoogle Scholar
  88. 88.
    Wang X, Lai YC, Lai CH (2007) Phys Rev E75:056205CrossRefGoogle Scholar
  89. 89.
    Zhou C, Kurths J (2006) Phys Rev Lett 96:164102CrossRefGoogle Scholar
  90. 90.
    Huang D (2006) Phys Rev E 74:046208MathSciNetCrossRefGoogle Scholar
  91. 91.
    Boccaletti S, Hwang DU, Chavez M, Amann A, Kurths J, Pecora LM (2006) Phys RevE 74:016102MathSciNetCrossRefGoogle Scholar
  92. 92.
    Zhao M, Zhou T, Wang BH, Wang WX (2005) Phys Rev E72:057102CrossRefGoogle Scholar
  93. 93.
    Barthélemy M (2004) Eur Phys J B 38:163Google Scholar
  94. 94.
    Zhou T, Zhao M, Wang BH (2006) Phys Rev E73:037101CrossRefGoogle Scholar
  95. 95.
    Bondy JA, Murty USR (1976) Graph Theory with Applications.MacMillan,LondonMATHGoogle Scholar
  96. 96.
    Bollobás B (1998) Modern Graph Theory.Springer, NewYorkGoogle Scholar
  97. 97.
    Xu JM (2003) Theory and Application of Graphs.Kluwer,DordrechtMATHGoogle Scholar
  98. 98.
    Newman MEJ, Watts DJ (1999) Phys Rev E 60:7332CrossRefGoogle Scholar
  99. 99.
    Yin CY, Wang WX, Chen G, Wang BH (2006) Phys Rev E74:047102CrossRefGoogle Scholar
  100. 100.
    Comellas F, Gago S (2007) J Phys A Math Theor40:4483MathSciNetMATHCrossRefGoogle Scholar
  101. 101.
    Duan Z, Chen G, Huang L (2007) Phys Rev E 76:056103CrossRefGoogle Scholar
  102. 102.
    Duan Z, Chen G, Huang L (2007) Phys Lett A 372:3741MathSciNetCrossRefGoogle Scholar
  103. 103.
    Duan Z, Liu C, Chen G (2008)Physica D 237:1006MathSciNetMATHCrossRefGoogle Scholar
  104. 104.
    Friedland B (1986) Control System Design.McGraw-Hill, New YorkGoogle Scholar
  105. 105.
    Tsuneda A (2005) Int J Bifurc Chaos 15:1MathSciNetMATHCrossRefGoogle Scholar
  106. 106.
    Um J, Han SG, Kim BJ, Lee SI (2008)(unpublished)Google Scholar
  107. 107.
    Akyildiz IF, Su W, Sankarasubramaniam Y, Cayirci E (2002) Comput Netw38:393CrossRefGoogle Scholar
  108. 108.
    Oqren P, Fiorelli E, Leonard NE (2004) IEEE Trans Automat Contr49:1292CrossRefGoogle Scholar
  109. 109.
    Arai T, Pagello E, Parker LE (2002) IEEE Trans Robot Automat18:655CrossRefGoogle Scholar
  110. 110.
    Couzin LD, Krause J, Franks NR, Levin SA (2005) Nature433:513CrossRefGoogle Scholar
  111. 111.
    Zhang HT, Chen M, Zhou T (2007) arXiv:0707.3402
  112. 112.
    Arenas A, Díaz-Guilera A, Pérez-Vicente CJ (2006) Phys Rev Lett96:114102Google Scholar
  113. 113.
    Boccaletti S, Ivanchenko M, Latora V, Pluchino A, Rapisarda A (2007) PhysRev E 75:045102(R)CrossRefGoogle Scholar
  114. 114.
    Timme M (2007) Phys Rev Lett 98:224101CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Guanrong Chen
    • 1
  • Ming Zhao
    • 2
  • Tao Zhou
    • 2
  • Bing-Hong Wang
    • 2
    • 3
  1. 1.Department of Electronic EngineeringCity University of Hong KongHong KongChina
  2. 2.Department of Modern Physics and Nonlinear Science CenterUniversity of Science and Technology of ChinaHefei AnhuiChina
  3. 3.Institute of Complex Adaptive SystemsShanghai Academy of System ScienceShanghaiChina