Synergetics pp 293-314 | Cite as

Applications to Biology

  • Hermann Haken
Part of the Springer Series in Synergetics book series (SSSYN, volume 1)


In theoretical biology the question of cooperative effects and self-organization nowadays plays a central role. In view of the complexity of biological systems this is a vast field. We have selected some typical examples out of the following fields:
  1. 1)

    Ecology, population-dynamics

  2. 2)


  3. 3)




Activator Concentration Unstable Mode Prey Animal Complete Analogy Computer Solution 
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Ecology, Population Dynamics Stochastic Models for a Predator-Prey System

  1. For general treatments seeGoogle Scholar
  2. N. S. Goel, N. Richter-Dyn: Stochastic Models in Biology (Academic Press, New York 1974)Google Scholar
  3. D. Ludwig: In Lecture Notes in Biomathematics, Vol. 3: Stochastic Population Theories, ed. by S. Levin (Springer, Berlin-Heidelberg-New York 1974)CrossRefGoogle Scholar
  4. For a different treatment of the problem of this section seeGoogle Scholar
  5. V. T. N. Reddy: J. Statist. Phys. 13, 1 (1975)CrossRefGoogle Scholar

A Simple Mathematical Model for Evolutionary Processes

  1. The equations discussed here seem to have first occurred in the realm of laser physics, where they explained mode selection in lasers (H. Haken, H. Sauermann: Z. Phys. 173, 261 (1963)). The application of laser-type equations to biological processes was suggested byADSCrossRefGoogle Scholar
  2. H. Haken: Talk at the Internat. Conference From Theoretical Physics to Biology, ed. by M. Marois, Versailles 1969Google Scholar
  3. H. Haken: In From Theoretical Physics to Biology, ed. by M. Marois (Karger, Basel 1973)Google Scholar
  4. A comprehensive and detailed theory of evolutionary processes has been developed by M. Eigen: Die Naturwissenschaften 58, 465 (1971). With respect to the analogies emphasized in our book it is interesting to note that Eigen’s “Bewertungsfunktion” is identical with the saturated gain function (8.35) of multimode lasers.ADSCrossRefGoogle Scholar
  5. An approach to interpret evolutionary and other processes as games is outlined byGoogle Scholar
  6. M. Eigen, R. Winkler-Oswatitsch: Das Spiel (Piper, München 1975)Google Scholar
  7. An important new concept is that of hypercycles and, connected with it, of “quasi-species”Google Scholar
  8. M. Eigen, P. Schuster: Naturwissensch. 64, 541 (1977)ADSCrossRefGoogle Scholar

A Model for Morphogenesis

  1. We present here a model due to Gierer and Meinhardt cf.Google Scholar
  2. A. Gierer, M. Meinhardt: Biological pattern formation involving lateral inhibition. Lectures on Mathematics in the Life Sciences 7, 163 (1974)MathSciNetGoogle Scholar
  3. H. Meinhardt: The Formation of Morphogenetic Gradients and Fields. Ber. Deutsch. Bot. Ges. 87, 101 (1974)Google Scholar
  4. H. Meinhardt, A. Gierer: Applications of a theory of biological pattern formation based on lateral inhibition. J. Cell. Sci. 15, 321 (1974)Google Scholar
  5. H. Meinhardt: preprint 1976Google Scholar

Order Parameters and Morphogenesis

  1. We present here unpublished results by H. Haken and H. Olbrich.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

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