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Synergetics pp 305-326 | Cite as

Applications to Biology

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

Abstract

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)

    Evolution

     
  3. 3)

    Morphogenesis

     

Keywords

Activator Concentration Unstable Mode Prey Animal Complete Analogy Computer Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

Ecology, Population Dynamics. 10.2 Stochastic Models for a Predator-Prey System

  1. For general treatments see N. S. Goel, N. Richter-Dyn: Stochastic Models in Biology (Academic Press, New York 1974)Google Scholar
  2. For general treatments see D. Ludwig: In Lecture Notes in Biomathematics, Vol. 3: Stochastic Population Theories, ed. by S. Levin (Springer, Berlin-Heidelberg-New York 1974)Google Scholar
  3. For a different treatment of the problem of this section see 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)).ADSCrossRefGoogle Scholar
  2. The application of laser-type equations to biological processes was suggested by H. Haken: Talk at the Internat. Conference From Theoretical Physics to Biology, ed. by M. Marois, Versailles 1969Google Scholar
  3. see also 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 by M. Eigen, R. Winkler-Oswatitsch: Das Spiel (Piper, München 1975)Google Scholar
  6. An important new concept is that of hypercycles and, connected with it, of “quasi-species” M. Eigen, P. Schuster: Naturwissensch. 64, 541 (1977);ADSCrossRefGoogle Scholar
  7. An important new concept is that of hypercycles and, connected with it, of “quasi-species” M. Eigen, P. Schuster: Naturwissensch. 65, 7 (1978);ADSCrossRefGoogle Scholar
  8. An important new concept is that of hypercycles and, connected with it, of “quasi-species” M. Eigen, P. Schuster: Naturwissensch. 65, 341 (1978)ADSCrossRefGoogle Scholar

A Model for Morphogenesis

  1. We present here a model due to Gierer and Meinhardt cf. A. Gierer, M. Meinhardt: Biological pattern formation involving lateral inhibition. Lectures on Mathematics in the Life Sciences 7, 163 (1974)MathSciNetGoogle Scholar
  2. We present here a model due to Gierer and Meinhardt cf. H. Meinhardt: The Formation of Morphogenetic Gradients and Fields. Ber. Deutsch. Bot. Ges. 87, 101 (1974)Google Scholar
  3. We present here a model due to Gierer and Meinhardt cf. H. Meinhardt, A. Gierer: Applications of a theory of biological pattern formation based on lateral inhibition. J Cell. Sci. 15, 321 (1974)Google Scholar
  4. We present here a model due to Gierer and Meinhardt cf. H. Meinhardt: preprint 1976Google Scholar
  5. We present here a model due to Gierer and Meinhardt cf. H. Meinhardt: Models of Biological Pattern Formation (Academic, London 1982)Google Scholar

Order Parameter and Morphogenesis

  1. We present here results by H. Haken and H. Olbrich. J. Math. Biol. 6, 317 (1978)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

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

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