Skip to main content

Stochastic and Chaotic Processes in Biochemical Systems

  • Conference paper
Book cover From Chemical to Biological Organization

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 39))

Abstract

Nonlinear networks of biochemical reactions play a very important role in the regulatory circuits of a living cell [1,2]. Benno Hess and his school played a pioneering role in the exploration of the complicated time patterns which may appear in such networks [3–7]. It was shown that among regular also chaotic and stochastic patterns may be observed [4,5].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.G. Reich, E.E. Sel’kov: Energy Metabolism of the Cell (Academic Press, London 1981)

    Google Scholar 

  2. L. Rensing, N.I. Jaeger (eds.): Temporal Order, Springer Ser. Syn., Vol. 29 (Springer Verlag, Berlin, Heidelberg 1984)

    Google Scholar 

  3. B. Hess, B. Chance: Naturwissenschaften 46, 248 (1959)

    Article  ADS  Google Scholar 

  4. B. Hess, A. Boiteux: Ber. Bunsenges. Phys. Chem. 84, 346 (1980)

    Google Scholar 

  5. B. Hess, M. Markus: Ber. Bunsenges. Phys. Chem. 89, 642 (1985)

    Google Scholar 

  6. S.C. Müller, Th. Plesser, B. Hess: In Temporal Order, ed. by L. Rensing, N.I. Jaeger (Springer Verlag, Berlin, Heidelberg 1984) p. 194

    Google Scholar 

  7. M. Markus, S.C. Müller, B. Hess: Ber. Bunsenges. Phys. Chem 89, 651 (1985)

    Google Scholar 

  8. E.E Sel’kov: Eur. J. Biochem. 4, 79 (1968)

    Article  Google Scholar 

  9. Th. Schulmeister, E.E. Sel’kov: stud. biophys. 65, 121 (1977)

    Google Scholar 

  10. A.V. Tolstopyatenko, L. Schimansky-Geier: In Selforganization by Nonlinear Irreversible Processes, ed. by W. Ebeling and H. Ulbricht (Springer, Berlin, Heidelberg 1986) p. 76

    Chapter  Google Scholar 

  11. Th. Schulmeister: stud. biophys. 72, 205 (1978)

    Google Scholar 

  12. J.S. Nicolis, G. Mayer-Kress, G. Haubs: Z. Naturforsch. 38a, 1157 (1983)

    MathSciNet  Google Scholar 

  13. P. Grassberger, I. Proccacia: Physica 13D, 34 (1984)

    ADS  Google Scholar 

  14. H. Fujisaka: Prog. Theor. Phys. 71, 513 (1984)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. G. Haubs, H. Haken: Z. Phys. B 59, 459 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  16. H. Herzel, W. Ebeling, Th. Schulmeister: Z. Naturforsch. 42a, 136 (1987)

    MathSciNet  Google Scholar 

  17. G. Nicolis, I. Prigogine: Self-Organization in Nonequilibrium Systems (Wiley, New York 1977)

    MATH  Google Scholar 

  18. J.P. Eckmann, D. Ruelle: Rev. Mod. Phys. 57, 617 (1985)

    Article  MathSciNet  ADS  Google Scholar 

  19. E.N. Lorenz: J. Atmos. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

  20. H. Herzel, B. Pompe: Phys. Lett. 122A, 121 (1987)

    MathSciNet  ADS  Google Scholar 

  21. L.F. Olsen: Phys. Lett. 94A, 454 (1983)

    ADS  Google Scholar 

  22. A. Goldbeter, O Decroly: Am. J. Physiol. 245, R478 (1983)

    Google Scholar 

  23. P. Grassberger, I. Proccacia: Physica 9D, 189 (1983)

    ADS  Google Scholar 

  24. H. Herzel, Th. Schulmeister: Syst.Anal.-Mod.-Sim. 4, 105 (1987)

    MathSciNet  Google Scholar 

  25. B. Pompe, J. Kruscha, R.W. Leven: Z. Naturforsch. 41a, 801 (1986)

    MathSciNet  ADS  Google Scholar 

  26. W. Ebeling, H. Herzel: stud. biophys. 98, 147 (1983)

    Google Scholar 

  27. W. Ebeling, R. Feistel: Physik der Selbstoroanisation und Evolution (Akademie-Verlag, Berlin 1982)

    Google Scholar 

  28. R. Feistel, W. Ebeling: Physic 93A, 114 (1978)

    MathSciNet  ADS  Google Scholar 

  29. L. Schimansky-Geier, AV. Tolstopyatenko, W. Ebeling: Phys. Lett. 108A, 329 (1985)

    ADS  Google Scholar 

  30. H. Engel-Herbert, W. Ebeling, H. Herzel: In Temporal Order, ed. by L. Rensing, N.I. Jaeger (Springer, Berlin, Heidelberg 1984) p. 144

    Google Scholar 

  31. H. Malchow, L. Schimansky-Geier: Noise and Diffusion in Bistable Noneauili-brium Systems (Teubner-Verlag, Leipzig 1986)

    Google Scholar 

  32. W. Ebeling, H. Herzel, W. Richert, L. Schimansky-Geier: ZAMM 66, 141 (1986)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. J. Kurths, H. Herzel: Physica 25D, 165 (1987)

    ADS  Google Scholar 

  34. H. Herzel, W. Ebeling, L. Schimansky-Geier, E.E. Sel’kov: In Lotka-Volterra-Approach to Cooperation and Competition in Dynamical Systems, ed. by W. Ebeling and M. Peschel (Akademie-Verlag, Berlin 1985)

    Google Scholar 

  35. L. Arnold: In Fluctuations and Sensitivity in Nonequilibrium Systems, ed. by W. Horsthemke, D.K. Kondepudi (Springer, Berlin, Heidelberg 1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ebeling, W., Herzel, H., Schimansky-Geier, L. (1988). Stochastic and Chaotic Processes in Biochemical Systems. In: Markus, M., Müller, S.C., Nicolis, G. (eds) From Chemical to Biological Organization. Springer Series in Synergetics, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73688-9_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-73688-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-73690-2

  • Online ISBN: 978-3-642-73688-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics