The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 155–168 | Cite as

Multi-time-scale synchronization and information processing in bursting neuron networks

  • T. PereiraEmail author
  • M. S. Baptista
  • J. Kurths


We analyze the effect of synchronization in networks of chemically coupled multi-time-scale (spiking-bursting) neurons on the process of information transmission within the network. Although, synchronization occurs first in the slow time-scale (burst) and then in the fast time-scale (spike), we show that information can be transmitted with low probability of errors in both time scales when the bursts become synchronized. Furthermore, we show that for networks of non-identical multi-time-scales neurons, complete synchronization is no longer possible, but instead burst phase synchronization. Our analysis shows that clusters of burst phase synchronized neurons are very likely to appear in a network for parameters far smaller than the ones for which the onset of burst phase synchronization in the whole network takes place.


Lyapunov Exponent Coupling Strength European Physical Journal Special Topic Information Transmission Phase Synchronization 
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  1. M. Steriade, R.R. Llinas, Physiol. Rev. 68, 649 (1988) Google Scholar
  2. S.M. Sherman, C. Kock, Exp. Brain Res. 63, 1 (1986) Google Scholar
  3. E.R. Kandel, J.H. Schwartz, T.M. Jessel, Principles of Neural Science, 4th edn. (McGraw Hill, 2000) Google Scholar
  4. W. Schultz, J. Neurophysiol. 80, 1 (1998) Google Scholar
  5. A.S. Freeman, L.T. Meltzer, B.S. Bunney, Life Sci. 36, 1983 (1985) Google Scholar
  6. A.A. Grace, B.S. Bunney, Neuroscience 10, 2877 (1984) Google Scholar
  7. E. Rodriguez, N. George, J.P. Lachaux et al., Nature 397, 430 (1999) Google Scholar
  8. M. Stopfer, G. Laurent, Nature 402, 664 (1999) Google Scholar
  9. P. Fries, J.H. Reynolds, A.E. Rorie et al., Science 291, 1560 (2001) Google Scholar
  10. T. Seidenbecher, T. Rao Laxmi, O. Stork et al., Science 301, 846 (2003) Google Scholar
  11. P. Tass, M.G. Rosenblum, J.Weule et al., Phys. Rev. Lett. 81, 3291 (1998) Google Scholar
  12. F. Mormann, T. Kreuz, R.G. Andrzejak et al., Epilepsy Res. 53, 173 (2003) Google Scholar
  13. A. Borst, F.E. Theunissen, Nature Neurosci. 2, 947 (1999) Google Scholar
  14. J.J. Eggermont, Neurosc. Bio. Rev. 22, 355 (1998) Google Scholar
  15. A. Catteneo, L. Maffei, C. Morrone, Proc. Royal Soc. Lond. B 212, 279 (1981) Google Scholar
  16. S. Spinoza, Ethics Demonstrated in Geometrical Order, Part I (MTSU Phil. WebWorks Hypertext Edition, 1997) Google Scholar
  17. N.F. Rulkov, Phys. Rev. Lett. 86, 183 (2001) Google Scholar
  18. H. Fujisika, T. Yamada, Progr. Theoret. Phys. 69, 32 (1983) Google Scholar
  19. L.M. Pecora, T. Carrol, Phys. Rev. Lett. 64, 821 (1990) Google Scholar
  20. L.M. Pecora, T. Carrol, Phys. Rev. Lett. 80, 2109 (1998) Google Scholar
  21. S. Strogatz, Sync: The Emerging Science of Spontaneous Order (Hyperion, 2003) Google Scholar
  22. S. Boccaletti, J. Kurths, G. Osipov et al., Phys. Rep. 366, 1 (2002); J. Kurths, S. Boccaletti, C. Grebogi et al., Chaos 13, 126 (2003) Google Scholar
  23. A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlinear Sciences (Cambridge University Press, 2001) Google Scholar
  24. I. Leyva, E. Allaria, S. Boccaletti et al., Phys. Rev. E 68, 066209 (2003) Google Scholar
  25. I. Fischer, Y. Liu, P. Davis, Phys. Rev. A 62, 011801 (2000) Google Scholar
  26. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 76, 1804 (1996); A.S. Pikovsky, M.G. Rosenblum, J. Kurths, Physica D 76, 1804 (1997) Google Scholar
  27. U. Parlitz, L. Junge, W. Lauterborn et al., Phys. Rev. E 54, 2115 (1996) Google Scholar
  28. M.S. Baptista, T. Pereira, J.C. Sartorelli et al., Phys. Rev. E 67, 056212 (2003) Google Scholar
  29. I.Z. Kiss, J.L. Hudson, Phys. Rev. E 64, 046215 (2001) Google Scholar
  30. C.M. Ticos, E. Rosa Jr., W.B. Pardo et al., Phys. Rev. Lett. 85, 2929 (2000) Google Scholar
  31. S. Hayes, C. Grebogi, E. Ott et al., Phys. Rev. Lett. 73, 1781 (1994) Google Scholar
  32. T. Yalçinkaya, Y.C. Lai, Phys. Rev. Lett. 79, 3885 (1997) Google Scholar
  33. G.V. Osipov, M.V. Ivanchenko, J. Kurths et al., Phys. Rev. E 71, 056209 (2005) Google Scholar
  34. M. Dhamala, V.K. Jirsa, M. Ding, Phys. Rev. Lett. 92, 028101 (2004) Google Scholar
  35. R. Ellison, V. Gardner, J. Lepak et al., Inter. J. Bif. Chaos 15, 2283 (2005); W.J. Freeman, J.M. Barrie, J. Neurophys. 84, 1266 (2000) Google Scholar
  36. P.A. Tass, T. Fieseler, J. Dammers et al., Phys. Rev. Lett. 90, 088101 (2003) Google Scholar
  37. K. Josić, M. Beck, Chaos 13, 247 (2003); K. Josić, D.J. Mar, Phys. Rev. E 64, 056234 (2001) Google Scholar
  38. T. Pereira, M.S. Baptista, J. Kurths, Phys. Lett. A 362, 159 (2007) Google Scholar
  39. If the set \(\mathcal{D}\) is a subset of Φ, we say that \(\mathcal{D}\) localized (with respect to Φ) if there is a cross section Ψ and a neighborhood Λ of Ψ, such that \(\mathcal{D} \cup {\rm \Lambda} = \emptyset\). In particular, for practical detections, one may check whether \(\mathcal{D}\) is localized, by the following technique. If there is PS, for \({\bf y} \in \mathcal{D}\) it exists infinitely many \({\bf x} \in {\rm \Lambda}\) such that \({\bf y} \cap B_{\ell}({\bf x}) = \emptyset,\) where \(B_{\ell}({\bf x})\) is an open ball of radius ℓ centered at the point \({\bf x}\), and ℓ is small. Then, we may vary \({\bf y},{\bf x}\) (one may take \({\bf x}\) to be an arbitrary point of the attractor) and ℓ, to determine whether \(\mathcal{D}\) is localized Google Scholar
  40. M.S. Baptista, T. Pereira, J. Kurths, Physica D 216, 260 (2006) Google Scholar
  41. M.S. Baptista, T. Pereira, J.C. Sartorelli et al., Physica D 212, 216 (2005) Google Scholar
  42. T. Pereira, M.S. Baptista, J. Kurths, Europhys. Lett. 77, 40006 (2007) Google Scholar
  43. T. Pereira, M.S. Baptista, J. Kurths, Phys. Rev. E 75, 026216 (2007) Google Scholar
  44. T. Pereira, M.S. Baptista, M.B. Reyes et al., Onset of Phase Synchronization in Neurons Connected by Chemical Synapses, in IJBC (to appear) Google Scholar
  45. C.E. Shannon, The Bell Syst. Tech. J. 27, 623 (1948) Google Scholar
  46. M.S. Baptista, J. Kurths, Phys. Rev. E 72, 045202R (2005) Google Scholar
  47. J.L. Hindmarsh, R.M. Rose, Proc. R. Soc. Lond. B 221, 87 (1984); J.L. Hindmarsh, R.M. Rose, Nature 296, 162 (1982) Google Scholar
  48. H.J. Sommers, A. Crisanti, H. Sompolinsky et al., Phys. Rev. Lett. 60, 1895 (1988) Google Scholar
  49. I. Belykh, E. Lange, M. Hasler, Phys. Rev. Lett. 94, 188101 (2003) Google Scholar
  50. S. Hayes, C. Grebogi, E. Ott et al., Phys. Rev. Lett. 73, 1781 (1994) Google Scholar
  51. R. Borisyuk, G Borisyuk, Y. Kazanovich, Behav. Brain Sc. 21, 833 (1998) Google Scholar
  52. G.X. Qi, H.B. Huang, H.J. Wang et al., Europhys. Lett. 74, 733 (2006) Google Scholar
  53. R.D. Pinto, P. Varona, A.R. Volkovskii et al., Phys. Rev. E 62, 2644 (2000) Google Scholar
  54. S.W. Johnson, V. Seutin, R.A. North, Science 58, 665 (1992) Google Scholar
  55. C. Mulle, A. Madariaga, M. Deschenes, J. Neurosci. 6, 2134 (1986) Google Scholar
  56. A. Destexhe, Z.F. Mainen, T.J. Sejnowski, Neural Comput. 6, 14 (1994); A.A. Sharp, F.K. Skinner, E. Narder, J. Neurophysiol. 76, 867 (1996) Google Scholar
  57. I.N. Sneddon, Fourier Transforms (Dover, 1995) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Universität Potsdam, Institut für Physik Am Neuen Palais 10PotsdamGermany
  2. 2.Max-Planck-Institut für Physik Komplexer SystemeDresdenGermany

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