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Block structured dynamics and neuronal coding

J. M. González-Miranda

  • Departamento de Física Fundamental, Universidad de Barcelona, Avenida Diagonal 647, 08028 Barcelona, Spain

Phys. Rev. E 72, 051922 – Published 18 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.051922

Abstract

When certain control parameters of nervous cell models are varied, complex bifurcation structures develop in which the dynamical behaviors available appear classified in blocks, according to criteria of dynamical likelihood. This block structured dynamics may be a clue to understand how activated neurons encode information by firing spike trains of their action potentials.

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References (32)

  1. T. J. Sejnowski, Nature (London) 376, 21 (1995).
  2. E. E. Fetz, Science 278, 1901 (1997).
  3. D. Ferster and N. Spruston, Science 270, 756 (1995).
  4. A. V. Holden, Nature (London) 428, 382 (2004).
  5. M. J. Chacron, B. Lindner, and A. Longtin, Phys. Rev. Lett. 92, 080601 (2004).
  6. M. Abeles, Science 304, 523 (2004).
  7. Y. Ikegaya, G. Aaron, R. Cossart, D. Aronov, I. Lampl, D. Ferster, and R. Yuste, Science 304, 559 (2004).
  8. J. L. Hindmarsh and R. M. Rose, Proc. R. Soc. London, Ser. B 221, 87 (1984).
  9. A. L. Hodgkin and A. F. Huxley, J. Physiol. (London) 117, 500 (1952).
  10. A. I. Selverston, M. I. Rabinovich, H. D. I. Abarbanel, R. Elson, A. Szücs, R. D. Pinto, R. Huerta, and P. Varona, J. Physiol. (Paris) 94, 357 (2000).
  11. J. M. González-Miranda, Chaos 13, 845 (2003).
  12. S. Reinker, E. Puil, and R. M. Miura, Bull. Math. Biol. 65, 641 (2003).
  13. D. He, P. Shi, and L. Stone, Phys. Rev. E 67, 027201 (2003).
  14. R. Huerta, M. I. Rabinovich, H. D. I. Abarbanel, and M. Bazhenov, Phys. Rev. E 55, R2108 (1997).
  15. M. Dhamala, V. K. Jirsa, and M. Ding, Phys. Rev. Lett. 92, 028101 (2004).
  16. M. G. Rosenblum and A. S. Pikovsky, Phys. Rev. Lett. 92, 114102 (2004).
  17. I. Belykh, E. de Lange, and M. Hasler, Phys. Rev. Lett. 94, 188101 (2005).
  18. M. C. Eguia, M. I. Rabinovich, and H. D. I. Abarbanel, Phys. Rev. E 62, 7111 (2000).
  19. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations (Springer Verlag, New York, 1995).
  20. R. Fitzhugh, Biophys. J. 1, 445 (1961).
  21. H. G. Schuster, Deterministic Chaos (VCH Verlagsgesellschaft mbH, Weinheim, 1988).
  22. R. Badii, E. Brun, M. Finardi, L. Flepp, R. Holzner, J. Parisi, C. Reyl, and J. Simonet, Rev. Mod. Phys. 66, 1389 (1994).
  23. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77 (Cambridge University Press, Cambridge, UK, 1995).
  24. M. J. Chacron, A. Longtin, and L. Maler, J. Neurosci. 21, 5328 (2001).
  25. M. F. Bear, B. W. Connors, and M. A. Paradiso, Neuroscience: Exploring the Brain (Lippincott, Williams and Wilkins, Baltimore, MD, 2001).
  26. S. W. Kuffler, J. G. Nicholls, and R. K. Orkand, J. Neurophysiol. 29, 768 (1966).
  27. R. K. Orkand, J. G. Nicholls, and S. W. Kuffler, J. Neurophysiol. 29, 788 (1966).
  28. P. G. Haydon, Nat. Rev. Neurosci. 2, 185 (2001).
  29. J. M. González-Miranda, Synchronization and Control of Chaos (Imperial College Press, London, 2004).
  30. T. R. Chay, Physica D 16, 233 (1985).
  31. H. A. Braun, M. T. Huber, M. Dewald, K. Schäfer, and K. Voigt, Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 811 (1998).
  32. A. Sherman, J. Rinzel, and J. Keizer, Biophys. J. 54, 411 (1988).

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