Biochemistry (Moscow)

, Volume 68, Issue 10, pp 1109–1120 | Cite as

A Theoretical Graph Method for Search and Analysis of Critical Phenomena in Biochemical Systems. I. Graphical Rules for Detecting Oscillators

  • G. L. Ermakov


Sufficient conditions for existence of concentration oscillations of components of complex reactions are considered on the basis of graph theory. Graphical rules were developed for detecting oscillators in kinetic schemes of complex biochemical systems. The main types of topology and principles of construction of kinetic schemes of oscillators containing two, three, and four substances are considered. The resulting oscillators might be a part of the biochemical systems of the n-th order. Under certain conditions they were found to be capable of generating oscillations of the system components.

graph oscillations mathematical simulation 


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  1. 1.
    Ermakov, G. L., and Goldshtein, B. N. (2002) Biochemistry (Moscow), 67, 473-484.Google Scholar
  2. 2.
    Clark, B. L. (1974) J. Chem. Phys., 60, 1481-1492.Google Scholar
  3. 3.
    Clark, B. L. (1975) J. Chem. Phys., 62, 773-775.Google Scholar
  4. 4.
    Clark, B. L. (1975) J. Chem. Phys., 62, 3726-3738.Google Scholar
  5. 5.
    Volpert, A. I. (1972) Matemat. Sbornik, 88(130), 578-588.Google Scholar
  6. 6.
    Ivanova, A. N. (1979) Kinetika Kataliz, 20, 1019-1023.Google Scholar
  7. 7.
    Ivanova, A. N. (1979) Kinetika Kataliz, 20, 1024-1028.Google Scholar
  8. 8.
    Ivanova, A. N., and Ternopolsky, B. L. (1979) Kinetika Kataliz, 20, 1541-1548.Google Scholar
  9. 9.
    Quirk, J., and Ruppert, R. (1965) Rev. Econ. Stud., 32, 311-319.Google Scholar
  10. 10.
    Tyson, J. J. (1975) J. Chem. Phys., 62, 1010-1015.Google Scholar
  11. 11.
    Eigenberger, G. (1978) Chem. Eng. Sci., 33, 1255-1268.Google Scholar
  12. 12.
    Bykov, V. I., Yablonsky, G. S., and Kim, V. F. (1978) Dokl. Akad. Nauk SSSR, 242, 637-639.Google Scholar
  13. 13.
    Ivanova, A. N., Furman, G. A., Bykov, V. I., and Yablonsky, G. S. (1978) Dokl. Akad. Nauk SSSR, 242, 872-875.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2003

Authors and Affiliations

  • G. L. Ermakov
    • 1
  1. 1.Russian Academy of SciencesInstitute of Theoretical and Experimental BiophysicsPushchinoRussia

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