Noise-induced synchronization in bidirectionally coupled type-I neurons

The European Physical Journal B volume 74, pages 177–193 (2010)Cite this article

Abstract

We present here some studies on noise-induced order and synchronous firing in a system of bidirectionally coupled generic type-I neurons. We find that transitions from unsynchronized to completely synchronized states occur beyond a critical value of noise strength that has a clear functional dependence on neuronal coupling strength and input values. For an inhibitory-excitatory (IE) synaptic coupling, the approach to a partially synchronized state is shown to vary qualitatively depending on whether the input is less or more than a critical value. We find that introduction of noise can cause a delay in the bifurcation of the firing pattern of the excitatory neuron for IE coupling.

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References

  1. A.F. Huxley, A.L. Hodgkin, J. Physiol. (London) 117, 500 (1952)

    Google Scholar 

  2. H.C. Tuckwell, Stochastic Processes in Neurosciences (SIAM, Philadelphia, 1989)

  3. L. Morris, H. Lecar, Biophys. J. 35, 193 (1981)

    Google Scholar 

  4. D. Hansel, H. Sompolinsky, Phys. Rev. Lett. 68, 718 (1992)

    Google Scholar 

  5. W. Wang, G. Perez, H.A. Cerdeira, Phys. Rev. E 47, 2893 (1993)

    Google Scholar 

  6. F.E.-N. Hassan, M. Paulsamy, F.F. Fernando, H.A. Cerdeira, Chaos 19, 013103 (2009)

    Google Scholar 

  7. J.R. Rinzel, G.B. Ermentrout, in Methods of Neuronal Modeling, edited by C. Koch, I. Segev (MIT Press, Cambridge, MA, USA, 1989), pp. 135–169.

  8. C.V. Vreeswijk, L. Abbott, G.B. Ermentrout, J. Comp. Neuroscience 1, 313 (1994)

    Google Scholar 

  9. D. Hansel, G. Mato, C. Meunier, Neural Comput. 7, 307 (1995)

    Google Scholar 

  10. B. Ermentrout, Neural Comput. 8, 979 (1996)

    Google Scholar 

  11. C. Börgers, N. Kopell, Neural Comput. 15, 509 (2003)

    Google Scholar 

  12. C. Börgers, N. Kopell, Neural Comput. 17, 557 (2005)

    Google Scholar 

  13. E. Izhikevich, IEEE Trans. Neural Networks 10, 499 (1999)

    Google Scholar 

  14. W. Lim, S.-Y. Kim, J. Korean Physical Soc. 50, 219 (2007)

    Google Scholar 

  15. N. Malik, B. Ashok, J. Balakrishnan, Pramana- J. Phys. 74, 189 (2010).

    Google Scholar 

  16. C. Koch, Biophysics of Computation: Information processing in single neurons (Oxford University Press, NY, 1999)

  17. B. Gutkin, T. Hely, J. Jost, Neurocomputing 58, 753 (2004)

    Google Scholar 

  18. E. Kandel, J.H. Schwartz, T.M. Jessell, Principles of neural science (McGraw-Hill, New York, 2000)

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

  20. L.M. Pecora, T.L. Carroll, Phys. Rev. Lett. 64, 821 (1990)

    Google Scholar 

  21. C. Zhou, J. Kurths, Phys. Rev. Lett. 88, 230602 (2002)

    Google Scholar 

  22. V.S. Anishchenko, V.V. Astakhov, A.B. Neiman, T.E. Vadisova, L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems (Springer-Verlag, Berlin, 2002)

  23. R. Haberman, SIAM J. Appl. Math. 37, 69 (1979)

    Google Scholar 

  24. C. van den Broeck, P. Mandel, Phys. Lett. A 122, 36 (1987)

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Author information

Affiliations

  1. Potsdam Institute for Climate Impact Research, Telegrafenberg, 14412, Potsdam, Germany

    N. Malik

  2. Advanced Centre for Research in High Energy Materials (ACRHEM), University of Hyderabad, Central University PO, Gachi Bowli, Hyderabad -, 500 046, India

    B. Ashok

  3. School of Physics, University of Hyderabad, Central University PO, Gachi Bowli, Hyderabad -, 500 046, India

    J. Balakrishnan

Authors
  1. N. Malik
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  2. B. Ashok
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  3. J. Balakrishnan
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Correspondence to J. Balakrishnan.

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Malik, N., Ashok, B. & Balakrishnan, J. Noise-induced synchronization in bidirectionally coupled type-I neurons. Eur. Phys. J. B 74, 177–193 (2010). https://doi.org/10.1140/epjb/e2010-00073-x

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Keywords

  • Lyapunov Exponent
  • Coupling Strength
  • Instantaneous Frequency
  • Excitatory Neuron
  • Large Lyapunov Exponent