Mathematics in Medicine and the Life Sciences pp 211-239 | Cite as
Biological Clocks and Mechanisms of Neural Control
Chapter
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.
Annotated References
- 1.R. R. Ward, The living clocks, A. A. Knopf, New York, 1971.Google Scholar
- 2.A.J. Vander, J.H. Sherman, and D.S. Luciano, The mechanisms of body function, McGraw-Hill, 1975.Google Scholar
- 3.S.W. Kuffler, and J.G. Nicholls, From neuron to brain, Sinauer, Sunderlund, MA, 1976.Google Scholar
- 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.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.F.C. Hoppensteadt, An introduction to the mathematics of neurons, Cambridge Univ. Press, Cambridge, UK, 1986.Google Scholar
- 7.J.K. Hale, Ordinary differential equations, J. Wiley, New York, 1969.MATHGoogle Scholar
- 8.A.T. Winfree, The geometry of biological time, Springer—Verlag, New York, 1980.MATHGoogle Scholar
- 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.A.T. Winfree, When time breaks down, Princeton Univ. Press, 1987.Google Scholar
- 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.R. Guttman, L. Feldman, and E. Jakobsson, Frequency entrainment of squid axon membrane, J. Membrane Biol. 56 (1980), 9–18.CrossRefGoogle Scholar
- 13.H.C. Tuckwell, Introduction to theoretical neurobiology, Vols 1 and 2 Cambridge Univ. Press, New York, 1988.CrossRefGoogle Scholar
- 14.P. Horowitz and W. Hill, The art of electronics, Cambridge Univ. Press, New York, 1989.Google Scholar
- 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.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.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.D. Bramble, and D.R. Carrier, Running and breathing in mammals, Science 21 (1983), 251–256.CrossRefGoogle Scholar
- 19.F.C. Hoppensteadt, Intermittent chaos,PNAS, (USA) 86 (1989) 29912995.Google Scholar
- 20.C. von Euler, Central pattern generation during breathing, Trends in Neuroscience, Nov. 1980, 275–277.Google Scholar
- 21.F.C. Hopensteadt, The searchlight hypothesis, J. Math. Biol., 29 (1991), 689–691.CrossRefGoogle Scholar
- 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.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