Skip to main content

Cluster Synchronization

  • Chapter
  • First Online:
Synchronization in Networks of Nonlinear Circuits

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSNONLINCIRC))

  • 888 Accesses

Abstract

In this chapter, synchronization of a network into groups with distinct behavior is discussed. Both networks with heterogeneous units and networks with identical node dynamics are considered, and the peculiarities of this form of synchronization in the two cases are illustrated.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. C.O. Aguilar, B. Gharesifard, Almost equitable partitions and new necessary conditions for network controllability. Automatica 80, 25 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  2. I.S. Aranson, L. Kramer, The world of the complex Ginzburg–Landau equation. Rev. Mod. Phys. 74(1), 99 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. C. Godsil, G.F. Royle, Algebraic Graph Theory, vol. 207 (Springer Science & Business Media, Berlin, 2013)

    MATH  Google Scholar 

  4. M. Golubitsky, I. Stewart, D.G. Schaeffer, Singularities and Groups in Bifurcation Theory, vol. 2 (Springer Science & Business Media, Berlin, 2012)

    MATH  Google Scholar 

  5. J. Gómez-Gardenes, Y. Moreno, A. Arenas, Paths to synchronization on complex networks. Phys. Rev. Lett. 98(3), 034101 (2007)

    Article  Google Scholar 

  6. R. Gutiérrez, A. Amann, S. Assenza, J. Gómez-Gardenes, V. Latora, S. Boccaletti, Emerging meso-and macroscales from synchronization of adaptive networks. Phys. Rev. Lett. 107(23), 234103 (2011)

    Article  Google Scholar 

  7. V. Latora, V. Nicosia, G. Russo, Complex Networks: Principles, Methods and Applications (Cambridge University Press, Cambridge, 2017)

    Book  MATH  Google Scholar 

  8. W. Lin, H. Fan, Y. Wang, H. Ying, X. Wang, Controlling synchronous patterns in complex networks. Phys. Rev. E 93(4), 042209 (2016)

    Article  Google Scholar 

  9. W. Lin, H. Li, H. Ying, X. Wang, Inducing isolated-desynchronization states in complex network of coupled chaotic oscillators. Phys. Rev. E 94(6), 062303 (2016)

    Article  Google Scholar 

  10. N. O’Clery, Y. Yuan, G.B. Stan, M. Barahona, Observability and coarse graining of consensus dynamics through the external equitable partition. Phys. Rev. E 88(4), 042805 (2013)

    Google Scholar 

  11. D.J. Olinger, A low-dimensional model for chaos in open fluid flows. Phys. Fluids A Fluid Dyn. (1989–1993) 5(8), 1947–1951 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  12. L. M. Pecora, F. Sorrentino, A. M. Hagerstrom, T. E. Murphy, R. Roy, Cluster synchronization and isolated desynchronization in complex networks with symmetries. Nat. Commun. 5, 4079 (2014)

    Google Scholar 

  13. A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences, vol. 12 (Cambridge University Press, Cambridge, 2003)

    MATH  Google Scholar 

  14. M.T. Schaub, N. O’Clery, Y.N. Billeh, J.C. Delvenne, R. Lambiotte, M. Barahona, Graph partitions and cluster synchronization in networks of oscillators. Chaos Interdiscip. J. Nonlinear Sci. 26(9), 094821 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  15. F. Sorrentino, L.M. Pecora, A.M. Hagerstrom, T.E. Murphy, R. Roy, Complete characterization of the stability of cluster synchronization in complex dynamical networks. Sci. Adv. 2(4), e1501737 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mattia Frasca .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 The Author(s)

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Frasca, M., Gambuzza, L.V., Buscarino, A., Fortuna, L. (2018). Cluster Synchronization. In: Synchronization in Networks of Nonlinear Circuits. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-75957-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-75957-9_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-75956-2

  • Online ISBN: 978-3-319-75957-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics