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

  • Nefeli Dimitra Tsigkri-DeSmedt
  • Johanne Hizanidis
  • Eckehard Schöll
  • Philipp Hövel
  • Astero ProvataEmail author
Regular Article

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.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    Y. Kuramoto, D. Battogtokh, Nonlinear Phenom. Complex Syst. 5, 380 (2002)Google Scholar
  2. 2.
    D.M. Abrams, S.H. Strogatz, Phys. Rev. Lett. 93, 174102 (2004)ADSCrossRefGoogle Scholar
  3. 3.
    M.J. Panaggio, D. Abrams, Nonlinearity 28, R67 (2015)ADSCrossRefGoogle Scholar
  4. 4.
    E. Schöll, Eur. Phys. J. Spec. Top. 225, 891 (2016)CrossRefGoogle Scholar
  5. 5.
    C.R. Laing, C.C. Chow, Neural Comput. 13, 1473 (2001)CrossRefGoogle Scholar
  6. 6.
    H. Sakaguchi, Phys. Rev. E 73, 031907 (2006)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    I. Omelchenko, Y. Maistrenko, P. Hövel, E. Schöll, Phys. Rev. Lett. 106, 234102 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    J. Hizanidis, V. Kanas, A. Bezerianos, T. Bountis, Int. J. Bifurc. Chaos 24, 1450030 (2014)CrossRefGoogle Scholar
  9. 9.
    I. Omelchenko, O.E. Omel’chenko, P. Hövel, E. Schöll, Phys. Rev. Lett. 110, 224101 (2013)ADSCrossRefGoogle Scholar
  10. 10.
    I. Omelchenko, A. Provata, J. Hizanidis, E. Schöll, P. Hövel, Phys. Rev. E 91, 022917 (2015)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    J. Hizanidis, N.E. Kouvaris, G. Zamora-López, A. Díaz-Guilera, C.G. Antonopoulos, Sci. Rep. 6, 19845 (2016)ADSCrossRefGoogle Scholar
  12. 12.
    R.G. Andrzejak, C. Rummel, F. Mormann, K. Schindler, Sci. Rep. 6, 23000 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    N. Semenova, A. Zakharova, V. Anishchenko, E. Schöll, Phys. Rev. Lett. 117, 014102 (2016)ADSCrossRefGoogle Scholar
  14. 14.
    A. Vüllings, J. Hizanidis, I. Omelchenko, P. Hövel, New J. Phys. 16, 123039 (2014)CrossRefGoogle Scholar
  15. 15.
    N. Brunel, M.C.W. Van Rossum, Biol. Cybern. 97, 337 (2008)CrossRefGoogle Scholar
  16. 16.
    A. Zakharova, M. Kapeller, E. Schöll, Phys. Rev. Lett. 112, 154101 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    I. Schneider, M. Kapeller, S. Loos, A. Zakharova, B. Fiedler, E. Schöll, Phys. Rev. E 92, 052915 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    T. Banerjee, Europhys. Lett. 110, 60003 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    S.A.M. Loos, J.C. Claussen, E. Schöll, A. Zakharova, Phys. Rev. E 93, 012209 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    T. Banerjee, P. Sharathi Dutta, A. Zakharova, E. Schöll, Phys. Rev. E 94, 032206 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    I. Omelchenko, O. Omel’chenko, A. Zakharova, M. Wolfrum, E. Schöll, Phys. Rev. Lett. 116, 114101 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    J. Hizanidis, E. Panagakou, I. Omelchenko, E. Schöll, P. Hövel, A. Provata, Phys. Rev. E 92, 012915 (2015)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    S. Ulonska, I. Omelchenko, A. Zakharova, E. Schöll, Chaos 26, 094825 (2016)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    O. Omel’chenko, M. Wolfrum, S. Yanchuk, Yu. Maistrenko, O. Sudakov, Phys. Rev. E 85, 036210 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    Y. Maistrenko, O. Sudakov, O. Osiv, V. Maistrenko, New J. Phys. 17, 073037 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    A. Schmidt, T. Kasimatis, J. Hizanidis, A. Provata, P. Hövel, Phys. Rev. E 95, 032224 (2017)ADSCrossRefGoogle Scholar
  27. 27.
    R.A. Poldrack, M.J. Farah, Nature 526, 371 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    N.K. Logothetis, Nature 453, 869 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    P. Katsaloulis, D.A. Verganelakis, A. Provata, Fractals 17, 181 (2009)CrossRefGoogle Scholar
  30. 30.
    P. Expert, R. Lambiotte, D. Chialvo, K. Christensen, H.J. Jensen, D.J. Sharp, F. Turkheimer, J. R. Soc. Interface 8, 472 (2011)CrossRefGoogle Scholar
  31. 31.
    P. Katsaloulis, A. Ghosh, A.C. Philippe, A. Provata, R. Deriche, Euro. Phys. J. B 85, 150 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    E.S. Finn et al., Nat. Neurosci. 18, 1664 (2015)CrossRefGoogle Scholar
  33. 33.
    N.C. Rattenborg, C.J. Amlaner, S.L. Lima, Neurosci. Biobehav. Rev. 24, 817 (2000)CrossRefGoogle Scholar
  34. 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)ADSCrossRefGoogle Scholar
  35. 35.
    S. Luccioli, A. Politi, Phys. Rev. Lett. 105, 158104 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    S. Olmi, A. Politi, A. Torcini, Europhys. Lett. 92, 60007 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    N.D. Tsigkri-DeSmedt, J. Hizanidis, P. Hövel, A. Provata, Proc. Comput. Sci. 66, 13 (2015)CrossRefGoogle Scholar
  38. 38.
    N.D. Tsigkri-DeSmedt, J. Hizanidis, P. Hövel, A. Provata, Euro. Phys. J., Special Topics 225, 1149 (2016)ADSCrossRefGoogle Scholar
  39. 39.
    B. Ermentrout, Rep. Prog. Phys. 61, 353 (1998)ADSCrossRefGoogle Scholar
  40. 40.
    R.D. Vilela, B. Lindner, Phys. Rev. E 80, 031909 (2009)ADSCrossRefGoogle Scholar
  41. 41.
    B. Lindner, L. Schimansky-Geier, A. Longtin, Phys. Rev. E 66, 031916 (2002)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    N. Kouvaris, F. Müller, L. Schimansky-Geier, Phys. Rev. E 82, 061124 (2010)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    T. Isele, J. Hizanidis, A. Provata, P. Hövel, Phys. Rev. E 93, 022217 (2016)ADSCrossRefGoogle Scholar
  44. 44.
    S. Ruiz, N. Birbaumer, R. Sitaram, Front. Psychiatry 4, 17 (2013)CrossRefGoogle Scholar
  45. 45.
    E. Hannon et al., Nat. Neurosci. 19, 48 (2016)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute of Nanoscience and NanotechnologyAthensGreece
  2. 2.Section of Solid State Physics, Department of Physics, National and Kapodistrian University of AthensAthensGreece
  3. 3.Crete Center for Quantum Complexity and Nanotechnology, Department of Physics, University of CreteHeraklionGreece
  4. 4.Institut für Theoretische Physik, Technische Universität BerlinBerlinGermany
  5. 5.Bernstein Center for Computational Neuroscience Berlin, Humboldt-Universität zu BerlinBerlinGermany

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