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:
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1)
Ecology, population-dynamics
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2)
Evolution
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3)
Morphogenesis
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References
Ecology, Population Dynamics. 10.2 Stochastic Models for a Predator-Prey System
For general treatments see N. S. Goel, N. Richter-Dyn: Stochastic Models in Biology (Academic Press, New York 1974)
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)
For a different treatment of the problem of this section see V. T. N. Reddy: J. Statist. Phys. 13, 1 (1975)
A Simple Mathematical Model for Evolutionary Processes
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 by H. Haken: Talk at the Internat. Conference From Theoretical Physics to Biology, ed. by M. Marois, Versailles 1969
see also H. Haken: In From Theoretical Physics to Biology, ed. by M. Marois (Karger, Basel 1973)
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.
An approach to interpret evolutionary and other processes as games is outlined by M. Eigen, R. Winkler-Oswatitsch: Das Spiel (Piper, München 1975)
An important new concept is that of hypercycles and, connected with it, of “quasi-species” M. Eigen, P. Schuster: Naturwissensch. 64, 541 (1977);
An important new concept is that of hypercycles and, connected with it, of “quasi-species” M. Eigen, P. Schuster: Naturwissensch. 65, 7 (1978);
An important new concept is that of hypercycles and, connected with it, of “quasi-species” M. Eigen, P. Schuster: Naturwissensch. 65, 341 (1978)
A Model for Morphogenesis
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)
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)
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)
We present here a model due to Gierer and Meinhardt cf. H. Meinhardt: preprint 1976
We present here a model due to Gierer and Meinhardt cf. H. Meinhardt: Models of Biological Pattern Formation (Academic, London 1982)
Order Parameter and Morphogenesis
We present here results by H. Haken and H. Olbrich. J. Math. Biol. 6, 317 (1978)
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© 1983 Springer-Verlag Berlin Heidelberg
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Haken, H. (1983). Applications to Biology. In: Synergetics. Springer Series in Synergetics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88338-5_10
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