Advertisement

The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1281–1289 | Cite as

Reducing the number of time delays in coupled dynamical systems

  • Alexandre WagemakersEmail author
  • Javier Used
  • Miguel A. F. Sanjuán
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays

Abstract

When several dynamical systems interact, the transmission of the information between them necessarily implies a time delay. When the time delay is not negligible, the study of the dynamics of these interactions deserve a special treatment. We will show here that under certain assumptions, it is possible to reduce the number of time delays without altering the global dynamics. We will focus here on graphs of interactions with identical time delays and bidirectional connections. With these premises, it is possible to find a configuration where a number nz of time delays have been removed with nv − 1 ≤ nznv2 /4, where nv is the number of dynamical systems on a connected graph.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Yanchuck, G. Giacomelli, J. Phys. A: Math. Theor. 50, 103001 (2017) ADSCrossRefGoogle Scholar
  2. 2.
    M.C. Soriano, J. García-Ojalvo, C.R. Mirasso, I. Fischer, Rev. Mod. Phys. 85, 421 (2013) ADSCrossRefGoogle Scholar
  3. 3.
    R. Olfati-Saber, R.M. Murray, IEEE Trans. Autom. Control 49, 1520 (2004) CrossRefGoogle Scholar
  4. 4.
    X. Liang, M. Tang, M. Dhamala, Z. Liu, Phys. Rev. E 80, 066202 (2009) ADSCrossRefGoogle Scholar
  5. 5.
    C. Li, G. Chen, Phys. A: Stat. Mech. Appl. 343, 263 (2004) CrossRefGoogle Scholar
  6. 6.
    M.S. Yeung, S.H. Strogatz, Phys. Rev. Lett. 82, 648 (1999) ADSCrossRefGoogle Scholar
  7. 7.
    W.S. Lee, E. Ott, T.M. Antonsen, Phys. Rev. Lett. 103, 044101 (2009) ADSCrossRefGoogle Scholar
  8. 8.
    L. Lücken, J.P. Pade, K. Knauer, S. Yanchuk, EPL 103, 10006 (2013) CrossRefGoogle Scholar
  9. 9.
    L. Lücken, J. Pade, K. Knauer, SIAM J. Appl Dyn. Syst. 14, 286 (2015) MathSciNetCrossRefGoogle Scholar
  10. 10.
    A. Wagemakers, M. Sanjuán, Sci. Rep. 7, 2744 (2017) ADSCrossRefGoogle Scholar
  11. 11.
    M.X. Goemans, D.P. Williamson, J. ACM 42, 1115 (1995) CrossRefGoogle Scholar
  12. 12.
    M. Newman, Networks: an introduction (Oxford University Press, Oxford, UK, 2010) Google Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Alexandre Wagemakers
    • 1
    Email author
  • Javier Used
    • 1
  • Miguel A. F. Sanjuán
    • 1
    • 2
    • 3
  1. 1.Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan CarlosMadridSpain
  2. 2.Department of Applied InformaticsKaunas University of TechnologyKaunasLithuania
  3. 3.Institute for Physical Science and Technology, University of MarylandCollege ParkUSA

Personalised recommendations