Turbulent Morphogenesis of a Prototype Model Reaction-Diffusion System

  • Jürgen Parisi
  • Brigitte Röhricht
  • Joachim Peinke
  • Otto E. Rössler
Part of the NATO ASI Series book series (NSSA, volume 138)


Based on the well-established Rashevsky-Turing theory of morpho-genesis, we report on a simple two-cellular symmetrical reaction-diffusion model capable of eliciting symmetry-breaking phase transitions and boiling-type turbulence. Such self-organising cooperative processes are experimentally demonstrated with spatio-temporal nonlinear transport phenomena in semiconductors. The present reaction-diffusion model may acquire a rather general significance, as it represents the most convenient prototype model of many different synergetic systems in nature.


Nonequilibrium Phase Transition Constant Pool Lattice Heat Conductivity Move Charge Carrier Symmetrical Steady State 
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  1. [1]
    A. Gierer and H. Meinhardt, Kybernetik 12: 30 (1972).PubMedCrossRefGoogle Scholar
  2. [2]
    C.R. Kennedy and R. Aris, in “New Approaches to Nonlinear Problems in Dynamics”, P.J. Holmes, ed., SIAM, Philadelphia, p. 211 (1980).Google Scholar
  3. [3]
    H. Meinhardt and A. Gierer, J. Cell. Sci. 15: 321 (1974).PubMedGoogle Scholar
  4. [4]
    G. Nicolis and I. Prigogine, Self-organisation in Nonequilibrium Systems, Wiley, New York (1977).Google Scholar
  5. [5]
    J. Parisi, J. Peinke, B. Röhricht and R.P. Huebener, in “Proceedings of the 18th International Conference on the Physics of Semiconductors”, World Scientific, Singapore, p. 1571 (1986).Google Scholar
  6. [6]
    J. Peinke, A. Mühlbach, R.P. Huebener and J. Parisi, Phys. Lett. 108A: 407 (1985).CrossRefGoogle Scholar
  7. [7]
    J. Peinke, B. Röhricht, A. Mühlbach, J. Parisi, Ch. Nöldeke, R.P. Huebener and O.E. Rössler, Z. Naturforsch. 40a: 562 (1985)Google Scholar
  8. [8]
    J. Peinke, J. Parisi, B. Röhricht, B. Wessely and K.M. Mayer, Phys. Rev. Lett. (1987, to be published).Google Scholar
  9. [9]
    I. Prigogine and G. Nicolis, J. Chem. Phys. 46: 3542 (1967).CrossRefGoogle Scholar
  10. [10]
    N. Rashevsky, Bull Math. Biophys. 2: 15, 65, 109 (1940).CrossRefGoogle Scholar
  11. [11]
    B. Röhricht, B. Wessely, J. Peinke, A. Mühlbach, J. Parisi and R.P. Huebener, Physica 134B: 281 (1985).Google Scholar
  12. [12]
    B. Röhricht, J. Parisi, J. Peinke and O.E. Rössler, Z. Phys. B - Condensed Matter 65: 259 (1986).CrossRefGoogle Scholar
  13. [13]
    B. Röhricht, J. Parisi, J. Peinke and R.R. Huebener, Z. Phys. B -.Condensed Matter (1987, to be published).Google Scholar
  14. [14]
    O.E. Rössler, Z. Naturforsch. 31a: 1168 (1976).Google Scholar
  15. [15]
    O.E. Rössler and F.F. Seelig, Z. Naturforsch. 27b: 1444 (1972).Google Scholar
  16. [16]
    E. Schöll, J. Parisi, B. Röhricht, J. Peinke and R.P. Huebener, Phys. Lett. A 119A: 419 (1987).CrossRefGoogle Scholar
  17. [17]
    R. Shaw, The Dripping Faucet as a Model Chaotic System, Aerial Press, Santa Cruz (1985).Google Scholar
  18. [18]
    O. Sporns, S. Roth and F.F. Seelig, Physica D (1986, to be published).Google Scholar
  19. [19]
    A.M. Turing, Philos.Trans. R. Soc. London B 237: 37 (1952).Google Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Jürgen Parisi
    • 1
  • Brigitte Röhricht
    • 1
  • Joachim Peinke
    • 1
  • Otto E. Rössler
    • 2
  1. 1.Physikalisches Institut IIUniversität TübingenTübingenGermany
  2. 2.Institut für Physikalische und Theoretische ChemieUniversität TübingenTübingenGermany

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