, Volume 71, Issue 2, pp 195–201 | Cite as

Synchronization of networks

  • R. E. AmritkarEmail author


We study the synchronization of coupled dynamical systems on networks. The dynamics is governed by a local nonlinear oscillator for each node of the network and interactions connecting different nodes via the links of the network. We consider existence and stability conditions for both single- and multi-cluster synchronization. For networks with time-varying topology we compare the synchronization properties of these networks with the corresponding time-average network. We find that if the different coupling matrices corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand, for non-commuting coupling matrices the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.


Synchronization nonlinear dynamical systems networks 


05.45.Xt 89.75.-k 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S H Strogatz, Nature (London) 410, 268 (2001) and references thereinADSCrossRefGoogle Scholar
  2. [2]
    R Albert and A L Barabäsi, Rev. Mod. Phys. 74, 47 (2002) and references thereinADSCrossRefGoogle Scholar
  3. [3]
    D J Watts and S H Strogatz, Nature (London) 393, 440 (1998)CrossRefGoogle Scholar
  4. [4]
    A-L Barabäsi and R Albert, Science 286, 509 (1999)MathSciNetCrossRefGoogle Scholar
  5. [5]
    A Pikovsky, M Rosenblum and J Kurth, Synchronization: A universal concept in nonlinear dynamics (Cambridge University Press, Cambridge, 2001)zbMATHGoogle Scholar
  6. [6]
    S Boccaletti, J Kurth, G Osipov, D L Valladares and C S Zhou, Phys. Rep. 366, 1–2 (2002)zbMATHADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    Y Zhang, G Hu, H A Cerdeira, S Chen, T Braun and Y Yao, Phys. Rev. E63, 026211 (2001)Google Scholar
  8. [8]
    M G Rosenblum, A S Pikovsky and J Kurth, Phys. Rev. Lett. 76, 1804 (1996)ADSCrossRefGoogle Scholar
  9. [9]
    R E Amritkar and G Rangarajan, unpublishedGoogle Scholar
  10. [10]
    L M Pecora and T L Carroll, Phys. Rev. Lett. 80, 2109 (1998)CrossRefGoogle Scholar
  11. [11]
    S Jalan and R E Amritkar, Phys. Rev. Lett. 90, 014101 (2003)Google Scholar
  12. [12]
    S Jalan, R E Amritkar and C K Hu, Phys. Rev. E72, 016211, 016212 (2005)Google Scholar
  13. [13]
    D J Stilwell, E M Bollt and D G Roberson, nlin.CD/0502055Google Scholar
  14. [14]
    R E Amritkar and C K Hu, Chaos 16, 015117 (2006)Google Scholar

Copyright information

© Indian Academy of Sciences 2008

Authors and Affiliations

  1. 1.Physical Research LaboratoryNavrangapuraIndia

Personalised recommendations