Skip to main content
SpringerLink
Log in

Synchronization of networks

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S H Strogatz, Nature (London) 410, 268 (2001) and references therein

    Article  ADS  Google Scholar 

  2. R Albert and A L Barabäsi, Rev. Mod. Phys. 74, 47 (2002) and references therein

    Article  ADS  Google Scholar 

  3. D J Watts and S H Strogatz, Nature (London) 393, 440 (1998)

    Article  Google Scholar 

  4. A-L Barabäsi and R Albert, Science 286, 509 (1999)

    Article  MathSciNet  Google Scholar 

  5. A Pikovsky, M Rosenblum and J Kurth, Synchronization: A universal concept in nonlinear dynamics (Cambridge University Press, Cambridge, 2001)

    MATH  Google Scholar 

  6. S Boccaletti, J Kurth, G Osipov, D L Valladares and C S Zhou, Phys. Rep. 366, 1–2 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. Y Zhang, G Hu, H A Cerdeira, S Chen, T Braun and Y Yao, Phys. Rev. E63, 026211 (2001)

  8. M G Rosenblum, A S Pikovsky and J Kurth, Phys. Rev. Lett. 76, 1804 (1996)

    Article  ADS  Google Scholar 

  9. R E Amritkar and G Rangarajan, unpublished

  10. L M Pecora and T L Carroll, Phys. Rev. Lett. 80, 2109 (1998)

    Article  Google Scholar 

  11. S Jalan and R E Amritkar, Phys. Rev. Lett. 90, 014101 (2003)

    Google Scholar 

  12. S Jalan, R E Amritkar and C K Hu, Phys. Rev. E72, 016211, 016212 (2005)

    Google Scholar 

  13. D J Stilwell, E M Bollt and D G Roberson, nlin.CD/0502055

  14. R E Amritkar and C K Hu, Chaos 16, 015117 (2006)

Download references

Author information

Authors and Affiliations

  1. Physical Research Laboratory, Navrangapura, Ahmedabad, 380 009, India

    R. E. Amritkar

Authors
  1. R. E. Amritkar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. E. Amritkar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amritkar, R.E. Synchronization of networks. Pramana - J Phys 71, 195–201 (2008). https://doi.org/10.1007/s12043-008-0153-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12043-008-0153-6

Keywords

PACS Nos

Search

Navigation