Skip to main content
SpringerLink
Log in

Phase Dynamics on Small Hexagonal Lattices with Repulsive Coupling

  • Conference paper
Nonlinear Dynamics of Electronic Systems (NDES 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 438))

Included in the following conference series:

Abstract

We consider dynamics of identical phase oscillators on spatially periodic hexagonal lattices. Existence and stability properties of different clustering patterns are discussed and illustrated by numerical examples. In the case of the 4×4-lattice, the clustering pattern enables the existence of a constant of motion and, hence, of a continuous family of temporally periodic solutions.

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

Access this chapter

Log in via an institution
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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Golubitsky, M., Stewart, I.: Nonlinear dynamics of networks: The groupoid formalism. Bull. Amer. Math. Soc. 43(3), 305–364 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Wang, Y., Golubitsky, M.: Two-colour patterns of synchrony in lattice dynamical systems. Nonlinearity 18, 631–658 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  3. Antoneli, F., Dias, A.P.S., Golubitsky, M., Wang, Y.: Patterns of synchrony in lattice dynamical systems. Nonlinearity 18, 2193–2210 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Tsimring, L.S., Rulkov, N.F., Larsen, M.L., Gabbay, M.: Repulsive synchronization in an array of phase oscillators. Phys. Rev. Lett. 95, 014101 (2005)

    Google Scholar 

  5. Ionita, F., Labavić, D., Zaks, M.A., Meyer-Ortmanns, H.: Order-by-disorder in classical oscillator systems. The Eur. Phys. Journal B 86, 511 (2013)

    Article  Google Scholar 

  6. Shinomoto, S., Kuramoto, Y.: Phase transitions in active rotator systems. Progr. Theor. Phys. 75, 1105–1110 (1988)

    MathSciNet  Google Scholar 

  7. Kurrer, C., Schulten, K.: Noise-induced synchronous neuronal oscillations. Phys. Rev. E 51, 6213–6216 (1995)

    Google Scholar 

  8. Zaks, M.A., Neiman, A.B., Feistel, S., Schimansky-Geier, L.: Noise-controlled oscillations and their bifurcations in coupled phase oscillators. Phys. Rev. E 68, 066206 (2003)

    Google Scholar 

  9. Tessone, C.J., Mirasso, C.R., Toral, R., Gunton, J.D.: Diversity-induced resonance. Phys. Rev. Lett. 97, 194101 (2006)

    Article  Google Scholar 

  10. Aronson, D.G., Golubitsky, M., Mallet-Paret, J.: Ponies on a merry-go-round in arrays of Josephson junctions. Nonlinearity 4, 903–910 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  11. Watanabe, S., Strogatz, S.H.: Constants of motion for superconducting Josephson arrays. Physica D 74, 197–253 (1994)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Humboldt University of Berlin, Rudower Chaussee 25, 12489, Berlin, Germany

    Petar Tomov & Michael Zaks

Authors
  1. Petar Tomov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Zaks
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Technical University of Sofia, 8 St. Kl. Ohridski Blvd., 1000, Sofia, Bulgaria

    Valeri M. Mladenov

  2. Physics Department, Boston University, 590 Commonwealth Avenue, 02215, Boston, MA, USA

    Plamen Ch. Ivanov

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Tomov, P., Zaks, M. (2014). Phase Dynamics on Small Hexagonal Lattices with Repulsive Coupling. In: Mladenov, V.M., Ivanov, P.C. (eds) Nonlinear Dynamics of Electronic Systems. NDES 2014. Communications in Computer and Information Science, vol 438. Springer, Cham. https://doi.org/10.1007/978-3-319-08672-9_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08672-9_30

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08671-2

  • Online ISBN: 978-3-319-08672-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation