Advertisement

Biological Clocks and Mechanisms of Neural Control

  • Frank C. Hoppensteadt
  • Charles S. Peskin
Part of the Texts in Applied Mathematics book series (TAM, volume 10)

Abstract

A clock has three main parts: an oscillating system, such as a pendulum, spring, or electrical circuit; a source of energy; and a trigger mechanism or escapement that connects the energy source to the oscillator. A clock’s face presents the oscillator’s output in some useful way.

Keywords

Neural Control Biological Clock Spike Generator Neural Control Network Phase Reset 
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.

Annotated References

  1. 1.
    R. R. Ward, The living clocks, A. A. Knopf, New York, 1971.Google Scholar
  2. 2.
    A.J. Vander, J.H. Sherman, and D.S. Luciano, The mechanisms of body function, McGraw-Hill, 1975.Google Scholar
  3. 3.
    S.W. Kuffler, and J.G. Nicholls, From neuron to brain, Sinauer, Sunderlund, MA, 1976.Google Scholar
  4. 4.
    K. Hoffman, Splitting of circadian rhythms as a function of light intensity, Biochronometry, pp 134–151, National Academy of Sciences, Washington DC, 1971.Google Scholar
  5. 5.
    C. Rowesmitt, et al., Photoperiodic induction of diurnal locomotor activity in Microtus montanus, the montane vole, Can. J. Zool. 60 (1982), 2798–2803.Google Scholar
  6. 6.
    F.C. Hoppensteadt, An introduction to the mathematics of neurons, Cambridge Univ. Press, Cambridge, UK, 1986.Google Scholar
  7. 7.
    J.K. Hale, Ordinary differential equations, J. Wiley, New York, 1969.MATHGoogle Scholar
  8. 8.
    A.T. Winfree, The geometry of biological time, Springer—Verlag, New York, 1980.MATHGoogle Scholar
  9. 9.
    R. Guttman, S. Lewis, and J. Rinzel, Control of repetitive firing in squid axon membrane as a model for a neurone oscillation, J. Physiol. 305 (1980), 377–395.Google Scholar
  10. 10.
    A.T. Winfree, When time breaks down, Princeton Univ. Press, 1987.Google Scholar
  11. 11.
    A.L. Hodgson, and A.F. Huxley, A quantitivative description of membrane current and its application to conduction and excitation of nerve, J. Physiol. 117 (1952), 500–544.Google Scholar
  12. 12.
    R. Guttman, L. Feldman, and E. Jakobsson, Frequency entrainment of squid axon membrane, J. Membrane Biol. 56 (1980), 9–18.CrossRefGoogle Scholar
  13. 13.
    H.C. Tuckwell, Introduction to theoretical neurobiology, Vols 1 and 2 Cambridge Univ. Press, New York, 1988.CrossRefGoogle Scholar
  14. 14.
    P. Horowitz and W. Hill, The art of electronics, Cambridge Univ. Press, New York, 1989.Google Scholar
  15. 15.
    D.H. Perkel, J.H. Schulman, T.H. Bullock, G.P. Moore, and J.P. Segundo, Pace maker neurons: effects of regularly spaced synaptic input, Science 163 (1964), 61–63.CrossRefGoogle Scholar
  16. 16.
    J.E. Rose, J.F. Brugge, D.J. Anderson, and J.E. Hind, Phase-locked responses to low frequency tones in single auditory nerve fibers of the squirrel monkey, J. Neurophysiol. 30 (1967), 769–793.Google Scholar
  17. 17.
    C. Ascoli, M. Barbi, S. Chillemi, and D. Petracchi, Phase-locked responses in the Limulus lateral eye, Biophysical J. 19 (1977), 219–240.CrossRefGoogle Scholar
  18. 18.
    D. Bramble, and D.R. Carrier, Running and breathing in mammals, Science 21 (1983), 251–256.CrossRefGoogle Scholar
  19. 19.
    F.C. Hoppensteadt, Intermittent chaos,PNAS, (USA) 86 (1989) 29912995.Google Scholar
  20. 20.
    C. von Euler, Central pattern generation during breathing, Trends in Neuroscience, Nov. 1980, 275–277.Google Scholar
  21. 21.
    F.C. Hopensteadt, The searchlight hypothesis, J. Math. Biol., 29 (1991), 689–691.CrossRefGoogle Scholar
  22. 22.
    H.D. Patton, A.F. Fuchs, B. Hille, A. Scher, and R. Steiner, Textbook of physiology, Vol 1, W.B. Saunders, 1989.Google Scholar
  23. 23.
    F. Crick, Function of the thalamic reticular complex: the searchlight hypothesis, PNAS, (USA) 81 (1984), 4586–4590.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  • Charles S. Peskin
    • 2
  1. 1.College of Natural ScienceMichigan State UniversityEast LansingUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

Personalised recommendations