Skip to main content
SpringerLink
Log in

Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The effects of attracting-nonlocal and reflecting connectivity are investigated in coupled Leaky Integrate-and-Fire (LIF) elements, which model the exchange of electrical signals between neurons. Earlier investigations have demonstrated that repulsive-nonlocal and hierarchical network connectivity can induce complex synchronization patterns and chimera states in systems of coupled oscillators. In the LIF system we show that if the elements are nonlocally linked with positive diffusive coupling on a ring network, the system splits into a number of alternating domains. Half of these domains contain elements whose potential stays near the threshold and they are interrupted by active domains where the elements perform regular LIF oscillations. The active domains travel along the ring with constant velocity, depending on the system parameters. When we introduce reflecting coupling in LIF networks unexpected complex spatio-temporal structures arise. For relatively extensive ranges of parameter values, the system splits into two coexisting domains: one where all elements stay near the threshold and one where incoherent states develop, characterized by multi-leveled mean phase velocity profiles.

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. E. Schöll, Eur. Phys. J. Spec. Top. 225, 891 (2016)

    Article  Google Scholar 

  5. C.R. Laing, C.C. Chow, Neural Comput. 13, 1473 (2001)

    Article  Google Scholar 

  6. H. Sakaguchi, Phys. Rev. E 73, 031907 (2006)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. J. Hizanidis, V. Kanas, A. Bezerianos, T. Bountis, Int. J. Bifurc. Chaos 24, 1450030 (2014)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  11. J. Hizanidis, N.E. Kouvaris, G. Zamora-López, A. Díaz-Guilera, C.G. Antonopoulos, Sci. Rep. 6, 19845 (2016)

    Article  ADS  Google Scholar 

  12. R.G. Andrzejak, C. Rummel, F. Mormann, K. Schindler, Sci. Rep. 6, 23000 (2016)

    Article  ADS  Google Scholar 

  13. N. Semenova, A. Zakharova, V. Anishchenko, E. Schöll, Phys. Rev. Lett. 117, 014102 (2016)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  15. N. Brunel, M.C.W. Van Rossum, Biol. Cybern. 97, 337 (2008)

    Article  Google Scholar 

  16. A. Zakharova, M. Kapeller, E. Schöll, Phys. Rev. Lett. 112, 154101 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. T. Banerjee, Europhys. Lett. 110, 60003 (2015)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. T. Banerjee, P. Sharathi Dutta, A. Zakharova, E. Schöll, Phys. Rev. E 94, 032206 (2016)

    Article  ADS  Google Scholar 

  21. I. Omelchenko, O. Omel’chenko, A. Zakharova, M. Wolfrum, E. Schöll, Phys. Rev. Lett. 116, 114101 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  23. S. Ulonska, I. Omelchenko, A. Zakharova, E. Schöll, Chaos 26, 094825 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  24. O. Omel’chenko, M. Wolfrum, S. Yanchuk, Yu. Maistrenko, O. Sudakov, Phys. Rev. E 85, 036210 (2012)

    Article  ADS  Google Scholar 

  25. Y. Maistrenko, O. Sudakov, O. Osiv, V. Maistrenko, New J. Phys. 17, 073037 (2015)

    Article  ADS  Google Scholar 

  26. A. Schmidt, T. Kasimatis, J. Hizanidis, A. Provata, P. Hövel, Phys. Rev. E 95, 032224 (2017)

    Article  ADS  Google Scholar 

  27. R.A. Poldrack, M.J. Farah, Nature 526, 371 (2015)

    Article  ADS  Google Scholar 

  28. N.K. Logothetis, Nature 453, 869 (2008)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  30. 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 

  31. P. Katsaloulis, A. Ghosh, A.C. Philippe, A. Provata, R. Deriche, Euro. Phys. J. B 85, 150 (2012)

    Article  ADS  Google Scholar 

  32. E.S. Finn et al., Nat. Neurosci. 18, 1664 (2015)

    Article  Google Scholar 

  33. N.C. Rattenborg, C.J. Amlaner, S.L. Lima, Neurosci. Biobehav. Rev. 24, 817 (2000)

    Article  Google Scholar 

  34. N.C. Rattenborg, B. Voirin, S.M. Cruz, R. Tisdale, G. DellOmo, H.P. Lipp, M. Wikelski, A.L. Vyssotski, Nat. Commun. 7, 12468 (2016)

    Article  ADS  Google Scholar 

  35. S. Luccioli, A. Politi, Phys. Rev. Lett. 105, 158104 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  37. N.D. Tsigkri-DeSmedt, J. Hizanidis, P. Hövel, A. Provata, Proc. Comput. Sci. 66, 13 (2015)

    Article  Google Scholar 

  38. N.D. Tsigkri-DeSmedt, J. Hizanidis, P. Hövel, A. Provata, Euro. Phys. J., Special Topics 225, 1149 (2016)

    Article  ADS  Google Scholar 

  39. B. Ermentrout, Rep. Prog. Phys. 61, 353 (1998)

    Article  ADS  Google Scholar 

  40. R.D. Vilela, B. Lindner, Phys. Rev. E 80, 031909 (2009)

    Article  ADS  Google Scholar 

  41. B. Lindner, L. Schimansky-Geier, A. Longtin, Phys. Rev. E 66, 031916 (2002)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  43. T. Isele, J. Hizanidis, A. Provata, P. Hövel, Phys. Rev. E 93, 022217 (2016)

    Article  ADS  Google Scholar 

  44. S. Ruiz, N. Birbaumer, R. Sitaram, Front. Psychiatry 4, 17 (2013)

    Article  Google Scholar 

  45. E. Hannon et al., Nat. Neurosci. 19, 48 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Nefeli Dimitra Tsigkri-DeSmedt, Johanne Hizanidis & Astero Provata

  2. Section of Solid State Physics, Department of Physics, National and Kapodistrian University of Athens, Athens, Greece

    Nefeli Dimitra Tsigkri-DeSmedt

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

    Johanne Hizanidis

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

    Eckehard Schöll & Philipp Hövel

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

    Philipp Hövel

Authors
  1. Nefeli Dimitra Tsigkri-DeSmedt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johanne Hizanidis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eckehard Schöll
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Philipp Hövel
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Astero Provata
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Astero 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.D., Hizanidis, J., Schöll, E. et al. Chimeras in leaky integrate-and-fire neural networks: effects of reflecting connectivities. Eur. Phys. J. B 90, 139 (2017). https://doi.org/10.1140/epjb/e2017-80162-0

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2017-80162-0

Keywords

Search

Navigation