Advertisement

On the Variability of Timing in a Spatially Continuous System with Heterogeneous Connectivity

  • Viktor K. Jirsa
Chapter

Abstract

The processing of “relevant” or “meaningful” information has been related to the occurrence of macroscopic phase transitions in the system (see Jirsa (2004) [1] for a discussion). Information processing in a spatially distributed system is a function of the connectivity and the intrinsic dynamics of the elements constituting the system. The macroscopic phase transitions are influenced in particular by heterogeneous connections which connect far-distant sites. This type of connectivity is found commonly in biological systems such as the cortex. However, even before phase transitions occur, their signatures are present in a reduced variability of the timing patterns of the connected sites. Here we discuss how, and to what extent, the introduction of additional connectivity reduces the variability of timing patterns, even though the system does not perform a macroscopic phase transition.

Keywords

Spatial Mode Connectivity Matrix Intrinsic Dynamic Connection Topology Tensor Matrice 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V.K. Jirsa: Intern. Journ Bif. Chaos 14, 2 (2004)MathSciNetCrossRefGoogle Scholar
  2. 2.
    H. Haken: Synergetics. An Introduction 3rd ed. ( Springer, Berlin 1983 )MATHGoogle Scholar
  3. 3.
    M.C. Cross, P.C. Hohenberg: Rev. Mod. Phys. 65, 851 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    M. Hendrey, E. Ott, T.M. Antonsen Jr.: Phys. Rev. Lett. 82, 859 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    G.B. Ermentrout, N. Kopell: SIAM J. Appl. Math. 54, 478 (1994)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    V.K. Jirsa, J.A.S. Kelso: Phys. Rev E 62, 8462 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    V.K. Jirsa: Prog. Theo. Phys. Suppl. 139, 128 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    S. Amari: Biol. Cybern. 27, 77 (1977)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    P.L. Nunez: Neocortical Dynamics and Human EEG Rhythms, ( Oxford University Press, Oxford 1995 )Google Scholar
  10. 10.
    V.K. Jirsa, H. Haken: Phys. Rev. Lett. 77, 960 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    J.J. Wright, D.T.J. Liley: Behay. Brain. Sci. 19, 285 (1996)CrossRefGoogle Scholar
  12. 12.
    P.A. Robinson, C.J. Rennie, J.J. Wright: Phys. Rev. E 56, 826 (1997)ADSCrossRefGoogle Scholar
  13. 13.
    R. FitzHugh: Biophys. J. 1, 445 (1961)CrossRefGoogle Scholar
  14. 14.
    J. Nagumo, S. Arimoto, S. Yoshizawa: Proc. IRE 50, 2061 (1962)CrossRefGoogle Scholar
  15. 15.
    J.D. Murray: Mathematical Biology ( Springer, Berlin Heidelberg New York 1993 )MATHCrossRefGoogle Scholar
  16. 16.
    H.R. Wilson: Spikes, Decisions and Actions. (Oxford University Press, Oxford 1999 )Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Viktor K. Jirsa

There are no affiliations available

Personalised recommendations