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Reducing the number of time delays in coupled dynamical systems

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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 ≤ nz ≤ nv2 /4, where nv is the number of dynamical systems on a connected graph.

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References

  1. S. Yanchuck, G. Giacomelli, J. Phys. A: Math. Theor. 50, 103001 (2017)

    Article  ADS  Google Scholar 

  2. M.C. Soriano, J. García-Ojalvo, C.R. Mirasso, I. Fischer, Rev. Mod. Phys. 85, 421 (2013)

    Article  ADS  Google Scholar 

  3. R. Olfati-Saber, R.M. Murray, IEEE Trans. Autom. Control 49, 1520 (2004)

    Article  Google Scholar 

  4. X. Liang, M. Tang, M. Dhamala, Z. Liu, Phys. Rev. E 80, 066202 (2009)

    Article  ADS  Google Scholar 

  5. C. Li, G. Chen, Phys. A: Stat. Mech. Appl. 343, 263 (2004)

    Article  Google Scholar 

  6. M.S. Yeung, S.H. Strogatz, Phys. Rev. Lett. 82, 648 (1999)

    Article  ADS  Google Scholar 

  7. W.S. Lee, E. Ott, T.M. Antonsen, Phys. Rev. Lett. 103, 044101 (2009)

    Article  ADS  Google Scholar 

  8. L. Lücken, J.P. Pade, K. Knauer, S. Yanchuk, EPL 103, 10006 (2013)

    Article  Google Scholar 

  9. L. Lücken, J. Pade, K. Knauer, SIAM J. Appl Dyn. Syst. 14, 286 (2015)

    Article  MathSciNet  Google Scholar 

  10. A. Wagemakers, M. Sanjuán, Sci. Rep. 7, 2744 (2017)

    Article  ADS  Google Scholar 

  11. M.X. Goemans, D.P. Williamson, J. ACM 42, 1115 (1995)

    Article  Google Scholar 

  12. M. Newman, Networks: an introduction (Oxford University Press, Oxford, UK, 2010)

Download references

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Authors and Affiliations

  1. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Móstoles, Tulipán s/n, Madrid, 28933, Spain

    Alexandre Wagemakers, Javier Used & Miguel A. F. Sanjuán

  2. Department of Applied Informatics, Kaunas University of Technology, Studentu 50-415, Kaunas, 51368, Lithuania

    Miguel A. F. Sanjuán

  3. Institute for Physical Science and Technology, University of Maryland, College Park, MD, 20742, USA

    Miguel A. F. Sanjuán

Authors
  1. Alexandre Wagemakers
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  2. Javier Used
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  3. Miguel A. F. Sanjuán
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Correspondence to Alexandre Wagemakers.

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Wagemakers, A., Used, J. & Sanjuán, M.A.F. Reducing the number of time delays in coupled dynamical systems. Eur. Phys. J. Spec. Top. 227, 1281–1289 (2018). https://doi.org/10.1140/epjst/e2018-800044-x

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  • DOI: https://doi.org/10.1140/epjst/e2018-800044-x

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