Skip to main content
SpringerLink
Log in

Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity

  • Regular Article
  • Session B: Papers I
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

The effects of nonlocal and fractal connectivity are investigated in a network of Leaky Integrate-and-Fire (LIF) elements. The idea of fractal coupling originates from the hierarchical topology of networks formed by neuronal axons, which transmit the electrical signals in the brain. If a number of LIF elements with finite refractory period are nonlocally coupled, multi-chimera states emerge whose multiplicity depends both on the coupling strength and on the refractory period. We provide evidence that the introduction of a hierarchical topology in the coupling induces novel complex spatial and temporal structures, such as nested chimera states and transitions between multi-chimera states with different multiplicities. These results demonstrate new complex patterns, as well as transitions between different multi-chimera states arising from the combination of nonlinear dynamics with the hierarchical coupling.

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. A. Pikovsky, M.G. Rosenblum, J. Kurths, Synchronization, A Universal Concept in Nonlinear Sciences (Cambridge University Press, Cambridge, 2001)

  2. V.S. Anishchenko, V. Astakhov, A. Neiman, T. Vadivasova, L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems (Springer-Verlang, Berlin, 2007)

  3. V. Vuksanović, P. Hövel, NeuroImage 97, 1 (2014)

    Article  Google Scholar 

  4. V. Vuksanović, P. Hövel, Chaos 25, 023116 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  5. J. Ladenbauer, J. Lehnert, H. Rankoohi, T. Dahms, E. Schöll, K. Obermayer, Phys. Rev. E 88, 042713 (2013)

    Article  ADS  Google Scholar 

  6. Y. Kuramoto, D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002)

    Google Scholar 

  7. D.M. Abrams, S.H. Strogatz, Phys. Rev. Lett. 93, 174102 (2004)

    Article  ADS  Google Scholar 

  8. M.J. Panaggio, D.M. Abrams, Nonlinearity 28, R67 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  9. D.M. Abrams, S.H. Strogatz, Int. J. Bifurcation Chaos 16, 21 (2006)

    Article  MathSciNet  Google Scholar 

  10. D.M. Abrams, R.R. Mirollo, S.H. Strogatz, D.A. Wiley, Phys. Rev. E 101, 084103 (2008)

    Google Scholar 

  11. I. Omelchenko, O. Omel’chenko, P. Hövel, E. Schöll, Phys. Rev. Lett. 110, 224101 (2013)

    Article  ADS  Google Scholar 

  12. J. Hizanidis, V. Kanas, A.A. Bezerianos, T. Bountis, Int. J. Bifurcation Chaos 24, 1450030 (2013)

    Article  MathSciNet  Google Scholar 

  13. A. Vüllings, J. Hizanidis, I. Omelchenko, P. Hövel, J. Phys. 16, 123039 (2014)

    Google Scholar 

  14. I. Omelchenko, A. Provata, J. Hizanidis, E. Schöll, P. Hövel, Phys. Rev. E 91, 022917 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  15. N.D. Tsigkri-DeSmedt, J. Hizanidis, P. Hövel, A. Provata, Procedia Computer Sci. 66, 13 (2015)

    Article  Google Scholar 

  16. I. Schneider, M. Kapeller, S. Loos, A. Zakharova, B. Fiedler, E. Schöll, Phys. Rev. E 92, 052915 (2015)

    Article  ADS  Google Scholar 

  17. S.A.M. Loos, J.C. Claussen, E. Schöll, A. Zakharova, Phys. Rev. E 93, 012209 (2016)

    Article  ADS  Google Scholar 

  18. M.R. Tinsley, K. Showalter, Nat. Phys. 8, 662 (2012)

    Article  Google Scholar 

  19. A.M. Hagerstrom, T.E. Murphy, R. Roy, P. Hövel, I. Omelchenko, E. Schöll, Nat. Phys. 8, 658 (2012)

    Article  Google Scholar 

  20. M. Wickramasinghe, I.Z. Kiss, PLoS ONE 8, e80586 (2013)

    Article  ADS  Google Scholar 

  21. L. Larger, B. Penkovsky, Y. Maistrenko, Phys. Rev. Lett. 111, 054103 (2013)

    Article  ADS  Google Scholar 

  22. E.A. Martens, S. Thutupalli, A. Fourrière, O. Hallatschek, Proc. Nat. Acad. Sci. 110, 10563 (2013)

    Article  ADS  Google Scholar 

  23. N. Brunel, M.C.W. Van Rossum, Biol. Cybern. 97, 337 (2007)

    Article  Google Scholar 

  24. N. Kouvaris, F. Müller, L. Schimansky-Geier, Phys. Rev. E 82, 061124 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  25. S. Lucioli, A. Politi, Phys. Rev. E 105, 158104 (2010)

    Google Scholar 

  26. Q. Wang, G. Chen, M. Perc, PloS ONE 6, e15851 (2011)

    Article  ADS  Google Scholar 

  27. M. Nandan, C.R. Hens, P. Pal, S.K. Dana, Chaos 24, 043103 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  28. L. Tattini, S. Olmi, A. Torcini, Chaos 22, 023133 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  29. M. Zare, P. Grigolini, Phys. Rev. E 86, 051918 (2012)

    Article  ADS  Google Scholar 

  30. S. Olmi, A. Politi, A. Torcini, Europhys. Lett. 92, 60007 (2010)

    Article  ADS  Google Scholar 

  31. D.P. Rosin, D. Rontani, D. J. Gauthier, E. Schöll, Phys. Rev. Lett. 110, 104102 (2013)

    Article  ADS  Google Scholar 

  32. I. Omelchenko, Y. Maistrenko, P. Hövel, E. Schöll, Phys. Rev. Lett. 106, 234102 (2011)

    Article  ADS  Google Scholar 

  33. J. Hizanidis, E. Panagakou, E. Schöll, P. Hövel, A. Provata, Phys. Rev. E 92, 012915 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  34. P. Katsaloulis, D.A. Verganelakis, A. Provata, Fractals 17, 181 (2009)

    Article  Google Scholar 

  35. P. Katsaloulis, A. Ghosh, A.C. Philippe, A. Provata, R. Deriche, EPJ B 85, 150 (2012)

    Article  ADS  Google Scholar 

  36. P. Expert, R. Lambiotte, D. Chialvo, K. Christensen, H.J. Jensen, D.J. Sharp, F. Turkheimer, J. R. Soc. Interface 8, 472 (2011)

    Article  Google Scholar 

  37. P. Katsaloulis, J. Hizanidis, D.A. Verganelakis, A. Provata, Fluct. Noise Lett. 11, 1250032 (2012)

    Article  Google Scholar 

  38. J. Feder, Fractals (Plenum Press, New York, 1988)

Download references

Author information

Authors and Affiliations

  1. Institute of Nanoscience and Nanotechnology, National Center for Scientific Research “Demokritos”, 15310, Athens, Greece

    N.D. Tsigkri-DeSmedt, J. Hizanidis & A. Provata

  2. Department of Solid State Physics, Department of Physics, University of Athens, 15784, Athens, Greece

    N.D. Tsigkri-DeSmedt

  3. Crete Center for Quantum Complexity and Nanotechnology, Department of Physics, University of Crete, 71003, Heraklion, Greece

    J. Hizanidis

  4. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623, Berlin, Germany

    P. Hövel

  5. Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu Berlin, Philippstraße 13, 10115, Berlin, Germany

    P. Hövel

Authors
  1. N.D. Tsigkri-DeSmedt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Hizanidis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Hövel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Provata
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Provata.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tsigkri-DeSmedt, N., Hizanidis, J., Hövel, P. et al. Multi-chimera states and transitions in the Leaky Integrate-and-Fire model with nonlocal and hierarchical connectivity. Eur. Phys. J. Spec. Top. 225, 1149–1164 (2016). https://doi.org/10.1140/epjst/e2016-02661-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2016-02661-4

Search

Navigation