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Some Problems of Information Neurodynamics

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Radiophysics and Quantum Electronics Aims and scope

Abstract

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.

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REFERENCES

  1. H. R. Wilson, Spikes, Decision and Actions: Dynamical Foundations of Neuroscience, Oxford (1999).

  2. G. Deco and B. Schurmann, Phys. Rev. Lett., 79, 4697 (1997).

    Google Scholar 

  3. S.P. Strong, R. Koberle, R. R. De Ruyter Van Steveninck, and W. Bialek, Phys. Rev. Lett., 80, 197 (1998).

    Google Scholar 

  4. M. Stemmler and C. Koch, Nat. Neurosci., 2, 521 (1999).

    Google Scholar 

  5. A. Destexhe, Z. F. Mainen, and T. J. Sejnowski, Neural Comput., 6, 14 (1994).

    Google Scholar 

  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. A. E. Villa and M. Abeles, Brain Res., 509, 325 (1990).

    Google Scholar 

  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. R. Elson, A. I. Selverston, R. Huerta, M. I. Rabinovich, and H. D. I. Abarbanel, Phys. Rev. Lett., 81, 5692 (1998)

    Google Scholar 

  10. R. Elson, R. Huerta, H. D. I. Abarbanel, M. I. Rabinovich, and A. I. Selverston, J. Neurophysiol., 82, 115 (1999).

    Google Scholar 

  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. 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. 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. C. E. Shannon and W. Weaver, The Mathematical Theory of Communication, Univ. Illinois Press, Urbana (1949).

    Google Scholar 

  15. P. Dayan and L. F. Abbott, Theoretical Neuroscience, http://play.ccs.brandeis/~abbott/book/TOC.html

  16. F. Rieke, D. Warland, R. de Ruyter van Steveninck, and W. Bailek, Spikes, MIT Press (1997).

  17. V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Izv. Vyssh. Uchebn. Zaved., Radiofiz., 29, 1050 (1986).

    Google Scholar 

  18. J. F. Heagy, L.M. Pecora, and T. L. Carrol, Phys. Rev. E, 50, 1874 (1994).

    Google Scholar 

  19. N. F. Rulkov and A. R. Volkovskii, Phys. Lett. A, 179, 332 (1993).

    Google Scholar 

  20. A. Selverston, Progr. Brain Res., 123 247 (1999).

    Google Scholar 

  21. R. Huerta, P. Varona, M. I. Rabinovich, and H. D. I. Abarbanel, Biol. Cybern., 84, L1 (2001)

    Google Scholar 

  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).

  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. J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London, B221, 87 (1984).

    Google Scholar 

  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. A. I. Selverston, and M. Moulins, The Crustacean Stomatogastric System, Springer, Berlin (1987).

    Google Scholar 

  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. P. A. Getting, Ann. Rev. Neurosci., 12, 185 (1989).

    Google Scholar 

  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 http://inls.ucsd.edu/∼rpinto.

  30. R. R. Klevecz and F. H. Ruddle, Science, 159 634 (1968).

    Google Scholar 

  31. B. Novak and J. M. Mitchison, J. Cell Sci., 86 191 (1986).

    Google Scholar 

  32. R. Huerta, M. Bazhenov and M. I. Rabinovich, Europhys. Lett., 43, 719 (1998).

    Google Scholar 

  33. H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. S. Tsimring, Rev. Mod. Phys., 64, 1331 (1993).

    Google Scholar 

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

    Google Scholar 

  35. M. I. Rabinovich, J. J. Torres, P. Varona, R. Huerta, and P. Weidman, Phys. Rev. E, 60, R1130 (1999).

    Google Scholar 

  36. A. V. Gaponov-Grekhov and M. I. Rabinovich, Chaos, 6 259 (1996).

    Google Scholar 

  37. A. J. Hudspeth and N. K. Legothetis, Curr. Opin. Neurobiol., 10, 631 (2000).

    Google Scholar 

  38. G. Buzsaki and J. J. Chrobak, Curr. Opin. Neurobiol., 5, 504 (1995).

    Google Scholar 

  39. W. Singer and C. M. Gray, Ann. Rev. Neurosc., 18, 555 (1995).

    Google Scholar 

  40. R. M. May and W. I. Leonard, SIAM J. Applied Math., 29, 243 (1975).

    Google Scholar 

  41. S. Grossberg, J. Theor. Biol., 73, 101 (1978).

    Google Scholar 

  42. D. Desmaisons, J.-D. Vincent, and J.-M. Lledo, J. Neurosc., 19, 10727 (1999).

    Google Scholar 

  43. A. Afraimovich and M. I. Rabinovich, in preparation.

  44. M. Stopfer and G. Laurent, Nature, 402 664 (1999).

    Google Scholar 

  45. E. Vaadia, I. Haalman, M. Abeles, H. Bergman, Y. Prut, H. Slovin, and A. Aertsen, Nature 373, 515 (1995)

    Google Scholar 

  46. J. A. Vastano and H. L. Swinney, Phys. Rev. Lett., 60, 1773 (1988).

    Google Scholar 

  47. T. Schreiber, Phys. Rev. Lett., 85, 461 (2000).

    Google Scholar 

  48. M. C. Eguia, M. I. Rabinovich, and H. D. I. Abarbanel, Phys. Rev. E 62 7111 (2000).

    Google Scholar 

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Authors and Affiliations

  1. Institute for Nonlinear Science University of California, San Diego, La Jolla, California, USA

    M. I. Rabinovich, R. D. Pinto & R. Huerta

  2. Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia

    M. I. Rabinovich

  3. E.T.S. Informática, Universidad Autónoma de Madrid, Madrid, Spain

    R. Huerta

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  1. M. I. Rabinovich
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  2. R. D. Pinto
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  3. R. Huerta
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Rabinovich, M.I., Pinto, R.D. & Huerta, R. Some Problems of Information Neurodynamics. Radiophysics and Quantum Electronics 44, 403–427 (2001). https://doi.org/10.1023/A:1017997113898

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