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Dynamics and kinematics of simple neural systems

Chaos 6, 288 (1996); doi:10.1063/1.166176

Issue Date: September 1996

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Mikhail Rabinovich
Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402
Institute of Applied Physics, Russian Academy of Science, Nizhniy Novgorod, 603600, Russia

Allen Selverston
Department of Biology, University of California, San Diego, La Jolla, California 92093-0357

Leonid Rubchinsky
Institute for Nonlinear Science and Department of Physics, University of California, San Diego, La Jolla, California 92093-0402

Ramón Huerta
Institute for Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402
The dynamics of simple neural systems is of interest to both biologists and physicists. One of the possible roles of such systems is the production of rhythmic patterns, and their alterations (modification of behavior, processing of sensory information, adaptation, control). In this paper, the neural systems are considered as a subject of modeling by the dynamical systems approach. In particular, we analyze how a stable, ordinary behavior of a small neural system can be described by simple finite automata models, and how more complicated dynamical systems modeling can be used. The approach is illustrated by biological and numerical examples: experiments with and numerical simulations of the stomatogastric central pattern generators network of the California spiny lobster. ©1996 American Institute of Physics.
History: Received 26 March 1996; accepted 10 July 1996
Permalink: http://link.aip.org/link/?CHAOEH/6/288/1
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KEYWORDS and PACS

Keywords
PACS
  • 87.10.+e
    Biological and medical physics General, theoretical, and mathematical biophysics (including logic of biosystems, quantum biology, and relevant aspects of thermodynamics, information theory, cybernetics, and bionics)
  • 05.45.+b
    Statistical physics and thermodynamics Theory and models of chaotic systems
  • YEAR: 1996

PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (38)
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  1. H. D. I. Abarbanel, M. I. Rabinovich, A. I. Selverston, M. V. Bazhenov, R. Huerta, M. M. Sushchik, and L. L. Rubchinsky, “Synchronization in neuronal ensemblies,” Usp. Fiz. Nauk (Phys. Usp.) 166(4), 363–390 (1996).
  2. Y. I. Arshavsky, I. N. Beloozerova, G. N. Orlovsky, Y. V. Panchin, and G. A. Pavlova, “Control of locomotion in marine mollusc Clione limacina. II. Rhythmic neurons of pedal ganglia,” Exp. Brain Res. 58, 263–272 (1985).
  3. Y. V. Panchin, Y. I. Arshavsky, A. Selverston, and T. A. Cleland, “Lobster stomatogastric neurons in primary culture I. Basic characteristics,” J. Neurophys. 69, 1976–1992 (1993).
  4. T. Bal, F. Nagy, and M. Moulins, “Muscarinic modulation of a patterngenerating network: Control of neuronal properties,” J. Neurosci. 14, 3019–3035 (1994).
  5. H. D. I. Abarbanel, R. Huerta, M. I. Rabinovich, N. F. Rulkov, P. F. Rowat, and A. I. Selverston, “Synchronized action of synaptically coupled chaotic neurons,” to appear in Neural Computations.
  6. R. Thomas and R. D'Ari, Biological Feedback (Chemical Rubber, Boca Raton, 1990).
  7. Dynamic Biological Networks: The Stomatogastric Nervous System, edited by R. M. Harris-Warrick, E. Marder, M. Moulins, and A. I. Selverston (MIT Press, Cambridge, MA 1992).
  8. The Crustacean Stomatogastric System, edited by A. I. Selverston and M. Moulins (Springer-Verlag, Berlin, 1987).
  9. J. P. Miller, “Pyloric mechanisms,” in Ref. 8, pp. 109–136.
  10. T. Bal, F. Nagy, and M. Moulins, “The pyloric central pattern generator in Crustacea: a set of conditional neuronal oscillators,” J. Comp. Physiol. A 163, 715–727 (1988).
  11. R. C. Elson and A. I. Selverston, “Mechanisms of gastric rhythm generation in the isolated stomatogastric ganglion of spiny lobster: Bursting pacemaker potentials, synaptic interactions, and muscarinic modulation,” J. Neurophys. 68, 890–907 (1992).
  12. R. J. MacGregor, Theoretical Mechanics of Biological Neural Networks (Harcourt Brace Jovanovich, Boston, 1993).
  13. H. Hayashi and S. Ishizuka, “Chaotic nature of bursting discharges in the Onchidium pacemaker neuron,” J. Theor. Biol. 156, 269–291 (1992).
  14. F. Takens, in Dynamical Systems and Turbulence, edited by D. Rand and L. S. Young, Lecture Notes in Mathematics (Springer-Verlag, Berlin, 1981), Vol. 898, p. 366.
  15. H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer-Verlag, New York, 1996).
  16. A. L. Hodgkin and A. F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerve,” J. Physiol. (London) 117, 500–544 (1952).
  17. F. Buchholtz, J. Golowasch, I. R. Epstein, and E. Marder, “Mathematical model of an identified stomatogastric ganglion neuron,” J. Neurophys. 67, 332–340 (1992).
  18. J. Guckenheimer, S. Gueron, and R. M. Harris-Warrick, Philos. Trans. R. Soc. London Ser. B 341, 345–359 (1993).
  19. C. C. Canavier, J. W. Clark, and J. H. Byrne, “Simulation of the bursting activity of neuron R15 in Aplysia: Role of ionic currents, calcium balance, and modulatory transmitters,” J. Neurophys. 66, 2107–2124 (1991).
  20. Methods in Neuronal Modelling, edited by C. Koch and I. Segev (MIT Press, Cambridge, MA, 1989).
  21. Single Neuron Computation, edited by T. McKenna, J. Davis, and S. F. Zornetzer (Academic, Boston, 1992).
  22. T. R. Chay, “Chaos in a three-variable model of an excitable cell,” Physica D 16, 233–242 (1985).
  23. J. L. Hindmarsh and R. M. Rose, “A model of neuronal bursting using three coupled first order differential equations,” Proc. R. Soc. London Ser. B 221, 87–102 (1984).
  24. C. Morris and H. Lecar, “Voltage oscillations in the barnacle giant muscle fiber,” Biophys. J. 35, 193–213 (1981).
  25. H. Wilson and J. Cowan, “A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue,” Kybernetic 13, 55–80 (1973).
  26. R. Fitz Hygh, Biophys. J. 1, 445 (1961).
  27. J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE 50, 2061 (1962).
  28. L. F. Abbott and T. B. Kepler, “Model neurons: from Hodgkin-Huxley to Hopfield,” in Statistical Mechanics of Neural Networks, edited by L. Garrido (Springer-Verlag, Berlin, 1990).
  29. T. B. Kepler, L. F. Abbott, and E. Marder, “Reduction of conductancebased neuron models,” Biol. Cybern. 66, 381–387 (1992).
  30. L. Glass and D. A. Young, “Structure and dynamics of neural networks oscillators,” Brain Research 179, 207–218 (1979).
  31. G. B. Ermentrout and L. Edelstein-Keshet, “Cellular automata approaches to biological modelling,” J. Theor. Biol. 160, 97–133. (1993).
  32. W. S. McCulloch and W. H. Pitts, “Logical calculus of the ideas immanent in nervous activity,” Bull. Math. Biophys. 9, 127, (1943).
  33. R. Thomas, “An exercise with neurons,” Lect. Notes Biomath. 29, 388, (1979).
  34. D. Kleinfeld and H. Sompolinsky, “Associative network models for central pattern generators,” in Ref. 20, pp. 195–246.
  35. R. S. Thompson, “A model for basic pattern generating mechanisms in the lobster stomatogastric ganglion,” Biol. Cybern. 43, 71–78, (1982).
  36. R. Huerta, “A finite automata model of spiking-bursting neurons,” Int. J. Bifurcations Chaos 6, 705–714 (1996).
  37. M. Gola, “Bursting pacemaker neuron in mollusks: Slow cyclic variation of ionic conductances,” Pflügers Arch. 352, 17–36 (1974).
  38. A. A. Sharp, M. B. O'Neil, L. F. Abbott, and E. Marder, “Dynamics clamp: Computer generated conductances in real neurons,” J. Neurophys. 69, 992–995 (1993).

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