The European Physical Journal Special Topics

, Volume 225, Issue 1, pp 17–27 | Cite as

Phase switching in Hindmarsh-Rose relay neurons

  • Umeshkanta Singh Thounaojam
  • Pooja Rani Sharma
  • Manish Dev Shrimali
Regular Article Synchronization and Control in Time Delayed and other Networks
Part of the following topical collections:
  1. Synchronization and Control in Time-Delayed Complex Networks and Spatio-Temporal Patterns


A system of Hindmarsh-Rose relay neurons with time delay coupling is considered in which the relay (central) neuron has an additional feedback term that represents the interaction activity with a local environment. The strength of environmental coupling with the central neuron plays an important role in inducing synchronization and de-synchronization between the outer neurons. The strength of feedback developed from the environmental coupling has created a gradual quenching in the oscillations of the central neuron. At a higher feedback coupling strength, oscillation of the central neuron is suppressed drastically and a transition from a regime of synchronization to out-of-phase synchronization take place between the oscillations of the two outer neurons.


Coupling Strength European Physical Journal Special Topic Relay Network Membrane Voltage Central Neuron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization, A Universal Concept in Nonlinear Science (Cambridge University Press, Cambridge, 2001)Google Scholar
  2. 2.
    E. Rodriguez, N. George, J.P. Lachaux, J. Martinerie, B. Renault, F.J. Varela, Nature 397, 430 (1999)ADSCrossRefGoogle Scholar
  3. 3.
    W.H.R. Miltner, C. Braun, M. Arnold, H. Witte, E. Taub, Nature 397, 434, (1999)ADSCrossRefGoogle Scholar
  4. 4.
    A.K. Engel, P. König, A.K. Kreiter, T.B. Schillen, W. Singer, Trends Neurosci. 15, 218 (1992)CrossRefGoogle Scholar
  5. 5.
    U.S. Thounaojam, K. Manchanda, R. Ramaswamy, A. Bose, SIAM J. Appl. Dyn. Syst. 10, 987 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    B.B. Theyel, D.A. Llano, M. Sherman, Nat. Neurosci. 13, 84 (2010)CrossRefGoogle Scholar
  7. 7.
    L.L. Gollo, C.R. Mirasso, M. Atienza, M. Crespo-Garcia, J.L. Cantero, PLoS ONE 6(3), 17756 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    I. Fischer, R. Vicente, J.M. Buldú, M. Peil, C.R. Mirasso, M.C. Torrent, J.G. Ojalvo, Phys. Rev. Lett. 97, 123902(4) (2006)ADSCrossRefGoogle Scholar
  9. 9.
    F.M. Atay (ed.), Complex Time-Delay Systems (Springer-Verlag, Berlin, 2010)Google Scholar
  10. 10.
    H.G. Schuster, P. Wagne, Prog. Theor. Phys. 81, 939 (1989)ADSCrossRefGoogle Scholar
  11. 11.
    F.M. Atay, J. Jost, A. Wende, Phys. Rev. Lett. 92, 144101(4) (2004)ADSCrossRefGoogle Scholar
  12. 12.
    G. Saxena, A. Prasad, R. Ramaswamy, Phys. Rep. 521, 205 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    A. Prasad, M. Dhamala, B.M. Adhikari, R. Ramaswamy, Phys. Rev. E 81, 027201 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    D.V.R. Reddy, A. Sen, G.L. Johnston, Phys. Rev. Lett. 80, 5109(4) (1998)ADSCrossRefGoogle Scholar
  15. 15.
    D.V.R. Reddy, A. Sen, G. L. Johnston, Phys. Rev. Lett. 85, 3381(4) (2000)ADSCrossRefGoogle Scholar
  16. 16.
    F.M. Atay, Physica D 183, 1 (2003)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    D.J. Selkoe, Ann. N. Y. Acad. Sci. 924, 17 (2000)ADSCrossRefGoogle Scholar
  18. 18.
    F. Toschi, F. Lugli, F. Biscarini, F. Zerbetto, J. Phys. Chem. 113, 369 (2009)CrossRefGoogle Scholar
  19. 19.
    P.R. Sharma, A. Sharma, M.D. Shrimali, A. Prasad, Phys. Rev. E 83, 067201 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    J.L. Hindmarsh, R.M. Rose, Proc. R. Soc. Lond. B 221, 87 (1984)ADSCrossRefGoogle Scholar
  21. 21.
    K. Pyragas, Phys. Lett. A 170, 421 (1992)ADSCrossRefGoogle Scholar
  22. 22.
    K. Pyragas, Phil. Trans. R. Soc. A 364, 2309 (2006)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    J.D. Farmer, Physica D 4(3), 366 (1984)MathSciNetCrossRefGoogle Scholar
  24. 24.
    M. Dhamala, V.K. Jirsa, M. Ding, Phys. Rev. Lett. 92, 074104(4) (2004)ADSCrossRefGoogle Scholar
  25. 25.
    A. Bergner, M. Frasca, G. Sciuto, A. Buscarnino, E.J. Ngamga, L. Fortuna, J. Kurths, Phy. Rev. E 85, 026208 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    Z. Ma, G. Zhang, Y. Wang, Z. Liu, J. Phys. A: Math. Theor. 41, 155101 (2008)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    L. Chandrasekaran, S. Achuthan, C. Canavier Carmen, J. Comput. Neurosci. 30, 427 (2011)MathSciNetCrossRefGoogle Scholar
  28. 28.
    S. Achuthan, C. Canavier Carmen, J. Neurosci. 29(16), 5218 (2009)CrossRefGoogle Scholar
  29. 29.
    S.J.S. Theesar, M.R.K. Ariffin, S. Banerjee, Optics Laser Technol. 54, 15 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    D.G. Aronson, G.B. Ermentrout, N. Kopell, Physica D 41, 403 (1990)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    J.J. Collins, I.N. Stewart, J. Nonlin. Sci. 3, 349 (1993)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    P.J. Uhlhaas, D.E.J. Linden, W. Singer, C. Haenschel, M. Lindner, K. Maurer, E. Rodriguez, J. Neuerosci. 26, 8168 (2006)CrossRefGoogle Scholar
  33. 33.
    M.W. Howe, H.E. Atallah, A. McCool, D.J. Gibson, A.M. Graybiel, PNAS 108, 16801 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    L. Appeltant, G.V. Sande, J. Danckaert, I. Fischer, Nat. Sci. Reports 4, 3629(1–5) (2014)Google Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  • Umeshkanta Singh Thounaojam
    • 1
  • Pooja Rani Sharma
    • 1
  • Manish Dev Shrimali
    • 1
  1. 1.Department of PhysicsCentral University of RajasthanAjmerIndia

Personalised recommendations