Radiophysics and Quantum Electronics

, Volume 44, Issue 5–6, pp 403–427 | Cite as

Some Problems of Information Neurodynamics

  • M. I. Rabinovich
  • R. D. Pinto
  • R. Huerta


The goal of neural science is to understand the brain, how we perceive, move, think, and remember. All of these things are dynamical processes which are taking place in a complex, non-stationary and noisy environment. This means that these dynamical processes at all levels from small neural networks to behavior should be stable against perturbations but flexible and adaptive. The goal of neurodynamics is to formulate the main dynamical principles which can be a basis of such behavior and to predict the possible activities of neurons and neural ensembles using the tools of nonlinear dynamics. In this paper we discuss our last results related to the mostly challenging part of neurodynamics: information processing by dynamical neural ensembles.


Neural Network Information Processing Nonlinear Dynamic Dynamical Process Noisy Environment 
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.


  1. 1.
    H. R. Wilson, Spikes, Decision and Actions: Dynamical Foundations of Neuroscience, Oxford (1999).Google Scholar
  2. 2.
    G. Deco and B. Schurmann, Phys. Rev. Lett., 79, 4697 (1997).Google Scholar
  3. 3.
    S.P. Strong, R. Koberle, R. R. De Ruyter Van Steveninck, and W. Bialek, Phys. Rev. Lett., 80, 197 (1998).Google Scholar
  4. 4.
    M. Stemmler and C. Koch, Nat. Neurosci., 2, 521 (1999).Google Scholar
  5. 5.
    A. Destexhe, Z. F. Mainen, and T. J. Sejnowski, Neural Comput., 6, 14 (1994).Google Scholar
  6. 6.
    M. Abeles, H. Bergman, I. Gat, E. Seidelman, N. Tishby, and E. Vaadia, Proc. Natl. Acad. Sci. USA 92, 8616 (1995).Google Scholar
  7. 7.
    A. E. Villa and M. Abeles, Brain Res., 509, 325 (1990).Google Scholar
  8. 8.
    H. D. I. Abarbanel, R. Huerta, M. I. Rabinovich, N. F. Rulkov, P.F. Rowat, and A. I. Selverston, Neural Comput., 8, 1567 (1996).Google Scholar
  9. 9.
    R. Elson, A. I. Selverston, R. Huerta, M. I. Rabinovich, and H. D. I. Abarbanel, Phys. Rev. Lett., 81, 5692 (1998)Google Scholar
  10. 10.
    R. Elson, R. Huerta, H. D. I. Abarbanel, M. I. Rabinovich, and A. I. Selverston, J. Neurophysiol., 82, 115 (1999).Google Scholar
  11. 11.
    G. Laurent, M. Stopfer, R.W. Freidrich, M. Rabinovich, A. Volkovskii, and H. D. I. Abarbanel, Ann. Rev. Neurosc., 24, 263 (2001).Google Scholar
  12. 12.
    A. A. Andronov, E. A. Leontovitch, I. I. Gordon, and A. G. Maier, Theory of Bifurcations of Dynamical Systems on a Plane, Wiley, New York (1973).Google Scholar
  13. 13.
    A. A. Andronov, E. A. Leontovitch, I. I. Gordon, and A. G. Maier, Qualitative Theory of Dynamical Sys-tems of Second Order, Wiley, New York (1973).Google Scholar
  14. 14.
    C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, Univ. Illinois Press, Urbana (1949).Google Scholar
  15. 15.
    P. Dayan and L. F. Abbott, Theoretical Neuroscience, http://play.ccs.brandeis/~abbott/book/TOC.htmlGoogle Scholar
  16. 16.
    F. Rieke, D. Warland, R. de Ruyter van Steveninck, and W. Bailek, Spikes, MIT Press (1997).Google Scholar
  17. 17.
    V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 29, 1050 (1986).Google Scholar
  18. 18.
    J. F. Heagy, L.M. Pecora, and T. L. Carrol, Phys. Rev. E, 50, 1874 (1994).Google Scholar
  19. 19.
    N. F. Rulkov and A. R. Volkovskii, Phys. Lett. A, 179, 332 (1993).Google Scholar
  20. 20.
    A. Selverston, Progr. Brain Res., 123 247 (1999).Google Scholar
  21. 21.
    R. Huerta, P. Varona, M. I. Rabinovich, and H. D. I. Abarbanel, Biol. Cybern., 84, L1 (2001)Google Scholar
  22. 22.
    R. Huerta, R. D. Pinto, P. Varona, G. R. Stiesberg, M. I. Rabinovich, H. D. I. Abarbanel, and A. Selverston, Neural Networks (to be submitted).Google Scholar
  23. 23.
    R. M. Harris-Warrick, B. R. Johnson, J. H. Peck, P. Kloppenburg, A. Ayali, and J. Skarbinski, Ann. N.Y. Acad. Sci., 860, 155 (1998).Google Scholar
  24. 24.
    J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London, B221, 87 (1984).Google Scholar
  25. 25.
    R. D. Pinto, P. Varona, A. R. Volkovskii, A. Szücs, H. D. I. Abarbanel, and M. I. Rabinovich, Phys. Rev. E, 62, 2644 (2000).Google Scholar
  26. 26.
    A. I. Selverston, and M. Moulins, The Crustacean Stomatogastric System, Springer, Berlin (1987).Google Scholar
  27. 27.
    Y. I. Arshavsky, I.N. Beloozerova, G.N. Orlovsky, Y.V. Panchin, and G. A. Pavlova, Exp. Brain Res., 58, 255 (1985).Google Scholar
  28. 28.
    P. A. Getting, Ann. Rev. Neurosci., 12, 185 (1989).Google Scholar
  29. 29.
    R. D. Pinto, R. C. Elson, A. Szücs, M. I. Rabinovich, H. D. I. Abarbanel, and A. I. Selverston, J. Neu-rosc. Methods (2001) (to be submitted). Versions of the program including source code as well as more information about system requirements and schematics can be downloaded from∼rpinto.Google Scholar
  30. 30.
    R. R. Klevecz and F. H. Ruddle, Science, 159 634 (1968).Google Scholar
  31. 31.
    B. Novak and J. M. Mitchison, J. Cell Sci., 86 191 (1986).Google Scholar
  32. 32.
    R. Huerta, M. Bazhenov and M. I. Rabinovich, Europhys. Lett., 43, 719 (1998).Google Scholar
  33. 33.
    H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, Rev. Mod. Phys., 64, 1331 (1993).Google Scholar
  34. 34.
    L. M. Pecora and T. L. Carroll, Phys. Rev. Lett., 64, 821 (1990).Google Scholar
  35. 35.
    M. I. Rabinovich, J. J. Torres, P. Varona, R. Huerta, and P. Weidman, Phys. Rev. E, 60, R1130 (1999).Google Scholar
  36. 36.
    A. V. Gaponov-Grekhov and M. I. Rabinovich, Chaos, 6 259 (1996).Google Scholar
  37. 37.
    A. J. Hudspeth and N. K. Legothetis, Curr. Opin. Neurobiol., 10, 631 (2000).Google Scholar
  38. 38.
    G. Buzsaki and J. J. Chrobak, Curr. Opin. Neurobiol., 5, 504 (1995).Google Scholar
  39. 39.
    W. Singer and C. M. Gray, Ann. Rev. Neurosc., 18, 555 (1995).Google Scholar
  40. 40.
    R. M. May and W. I. Leonard, SIAM J. Applied Math., 29, 243 (1975).Google Scholar
  41. 41.
    S. Grossberg, J. Theor. Biol., 73, 101 (1978).Google Scholar
  42. 42.
    D. Desmaisons, J.-D. Vincent, and J.-M. Lledo, J. Neurosc., 19, 10727 (1999).Google Scholar
  43. 43.
    A. Afraimovich and M. I. Rabinovich, in preparation.Google Scholar
  44. 44.
    M. Stopfer and G. Laurent, Nature, 402 664 (1999).Google Scholar
  45. 45.
    E. Vaadia, I. Haalman, M. Abeles, H. Bergman, Y. Prut, H. Slovin, and A. Aertsen, Nature 373, 515 (1995)Google Scholar
  46. 46.
    J. A. Vastano and H. L. Swinney, Phys. Rev. Lett., 60, 1773 (1988).Google Scholar
  47. 47.
    T. Schreiber, Phys. Rev. Lett., 85, 461 (2000).Google Scholar
  48. 48.
    M. C. Eguia, M. I. Rabinovich, and H. D. I. Abarbanel, Phys. Rev. E 62 7111 (2000).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • M. I. Rabinovich
    • 1
    • 2
  • R. D. Pinto
    • 1
  • R. Huerta
    • 1
    • 3
  1. 1.Institute for Nonlinear Science University of CaliforniaSan Diego, La JollaUSA
  2. 2.Institute of Applied Physics of the Russian Academy of SciencesNizhny NovgorodRussia
  3. 3.E.T.S. InformáticaUniversidad Autónoma de MadridMadridSpain

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