Биологические ритмы. В 2-х т. Т. 1. Пер. с англ. €

_______________ Математические модели________________________ 85

ά на разность между какой-то переменной у и периодом Т, причем у следует за изменениями Т с запаздыванием. Ранее для этого эффекта был предложен конкретный биохимический механизм [18]; была показана достаточность этого предположения, по крайней мере для объяснения данных, полученных на Drosophila pseudoobscura [19].

Литература

1. Andronov Α. Α., Vitt Α. Α., Kaikin S. E. Theory of Oscillators, Oxford, Per-

gamon, 1966. '2. Engelmann W., Karlsson H. G., Johnsson A. Phase shifts in the kalanchoe

petal rhythm caused by light pulses of different durations, International J.

of Chronobiology, 1, 147—156 (1973).

3. Eskin A. Some properties of the system controlling the circadian activity rhythm of sparrows. In: M. Menaker (éd.), Biochronometry, Washington, D. C., National Academy of Sciences, 1971, pp. 55—80.

4. Johnsson A., Karlsson H. G. A feedback model for biological rhythms. I. Mathematical description and properties of the model, J. of Theoretical Biology, 36, 153—174 (1972).

5. Karlsson H. G., Johnsson A. A feedback model for biological rhythms. II. Comparisons with experimental results, especially on the petal rhythm of kalanchoe, J. of Theoretical Biology, 36, 175—194 (1972).

6. Minorsky N. Nonlinear Oscillations, Princeton, N. J., Van Nostrand, 1962.

7. Nicholis G., Portnow J. Chemical oscillations, Chemical Review, 73, 365— 384 (1973).

8. Njus D. Experimental approaches to membrane models. In: J. W. Hastings and H. G. Schweiger (eds.), The Molecular Basis of Circadian Rhythms, Berlin, Dahlem Konferenzen, 1976, pp. 283—294,

9. Njus D., Sulzman F. M., Hastings I. W. Membrane model for the circadian clock, Nature, 248, 116—120 (1974).

10. Pavlidis T. A mathematical model for the light affected system in the drosophila eclosion rhythm, Bulletin of Mathematical Biophysiology, 29, 291— 310 ,(1967).

11. Pavlidis T. Studies on biological clocks: A model for the circadian rhythms of nocturnal organisms. In: M. Gerstenhaber (éd.), Lectures on Mathematics in Life Sciences, Providence R. I., American Mathematical Society, 1968, pp. 88—112.

12. Pavlidis T. Populations of interacting oscillators and circadian rhythms, J. of Theoretical Biology, 22, 418—436 (1969).

13. Pavlidis T. Populations of biochemical oscillators as circadian clocks, J. of Theoretical Biology, 33, 319—338 (1971).

14. Pavlidis T. Biological Oscillators: Their Mathematical Analysis, New York, Academic Press, 1973.

15. Pavlidis T. The free run period of circadian rythsm 'and phase response curves, American Naturalist, 107, 524—530 (1973).

16. Pavlidis T. Spatial organization of chemical oscillators via an averaging operator, J. of Chemical Physics, 63, 5269—5273 (1975).

17. Pavlidis T. Spatial and temporal organization of populations of interacting oscillators. In: J. W. Hastings and H. G. Schweiger (eds.), The Molecular Basis of Circadian Rhythms, Berlin, Dahlem Konferenzen, 1976, pp. 131— 148.

18. Pavlidis T., Kauzmann W. Toward a quantitative biochemical model for circadian oscillators, Archives of Biochemistry and Biophysics, 132, 338—348 (1969).


Наши рекомендации