Temporal Disorder-Introductory Remarks

  • Ludger Rensing
  • Uwe an der Heiden
  • Michael C. Mackey
Part of the Springer Series in Synergetics book series (SSSYN, volume 36)


Those studying basic biological, chemical, and physical processes are quite accustomed to the marked periodic or aperiodic variations in certain variables important for system function and integrity (1,2). Like these phenomena, there are a variety of normal physiological processes that occur at regular, or almost regular, intervals. Abnormalities in many of these physiological rhythms are of major clinical importance. In addition, these oscillations demonstrate that there is a rich variety of dynamics that many physiological control systems can exhibit, ranging from rhythms with differing periodicities to irregular “noise-like” phenomena.


Physiological System Dynamical Disease Normal Physiological Process Irregular Oscillation Bifurcation Pattern 
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  1. 1.
    H. Haken (Ed): Dynamics of Synergetic Systems (Springer, Berlin, Heidelberg 1980)zbMATHGoogle Scholar
  2. 2.
    L. Rensing, N.I. Jaeger (Ed): Temporal Order (Springer, Berlin, Heidelberg 1985)zbMATHGoogle Scholar
  3. 3.
    H.A. Reimann: Periodic Diseases, F.A. Davis, Philadelphia (1963)Google Scholar
  4. 4.
    M.C. Mackey, L. Glass: Science 197, 287–289 (1977)ADSCrossRefGoogle Scholar
  5. 5.
    L. Glass, M.C. Mackey: Ann. N.Y. Acad. Sci. 316, 214–235 (1979)ADSCrossRefGoogle Scholar
  6. 6.
    M.C. Mackey, U. an der Heiden: Funk. Biol. Med. 1, 156–164 (1982)Google Scholar
  7. 7.
    M.C. Mackey, J.G. Milton: Proc. New York Acad. Sci., in pressGoogle Scholar
  8. 8.
    L. Glass, M.C. Mackey: From Clocks to Chaos: The Rhythms of Life, in pressGoogle Scholar
  9. 9.
    R.J. Konopka, S. Benzer: Proc. Natl. Acad. Sci. US 68, 2112 (1971)ADSCrossRefGoogle Scholar
  10. 10.
    J.P. Eckmann: Rev. Mod. Phys. 53, 643–654 (1981)MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 11.
    E. Ott: Rev. Mod. Phys. 53, 655–671 (1981)MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. 12.
    A. Lasota, M.C. Mackey: J. Math. Biology 19, 43–62 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    M.C. Mackey: In Temporal Order ed. by L. Rensing and N.I. Jaeger (Springer, Berlin, Heidelberg 1985) p. 1985Google Scholar
  14. 14.
    M.C. Mackey, M, Santavy, P. Selepova: In Nonlinear Oscillations in Biology and Chemistry, ed. by H. Othmer (Springer, Berlin, Heidelberg in press)Google Scholar
  15. 15.
    M. Kobayashi, T. Musha: IEEE Trans. Biomed. Eng. 29, 456–457 (1982)CrossRefGoogle Scholar
  16. 16.
    A.L. Goldberger, L.J. Findley, M.R. Blackburn, A.J. Mandell: Amer. Heart J. 107, 612–615 (1984)CrossRefGoogle Scholar
  17. 17.
    T.R. Chay, J. Rinzel: Biophys. J. 47, 357–366 (1985)CrossRefGoogle Scholar
  18. 18.
    P. LeBrun, I. Atwater: Biophys. J. 48, 529–531 (1985)CrossRefGoogle Scholar
  19. 19.
    J.-P. Eckmann, D. Ruelle: Rev. Mod. Phys. 57, 617–656 (1985)MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    A. Lasota, M.C. Mackey: Probabilistic Properties of Deterministic Systems. (Cambridge University Press, Cambridge 1985)zbMATHGoogle Scholar
  21. 21.
    L. Rensing: Biol. Rdsch. 24, 5–15 (1986)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Ludger Rensing
    • 1
  • Uwe an der Heiden
    • 2
  • Michael C. Mackey
    • 3
  1. 1.Fachbereich 2/BiologieUniversität BremenBremenFed. Rep. of Germany
  2. 2.Fakultät für NaturwissenschaftenUniversität Witten/HerdeckeWitten (Ruhr)Fed. Rep. of Germany
  3. 3.Department of PhysiologyMcGill UniversityMontrealCanada

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