The Rashevsky-Turing System: Two Coupled Oscillators as a Generic Reaction-Diffusion Model

  • M. Klein
  • G. Baier
  • O. E. Rössler
Conference paper

Abstract

A two-compartment reaction-diffusion system is investigated both analytically and numerically. Owing to the system’s symmetry, a complete characterization of the three fixed points and their respective stability is achieved. Dependent on the coupling strength, different types of chaos can be observed in computer simulations. Some implications of the model are pointed out.

Keywords

Germanium Subsy 

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References

  1. [1]
    N. Rashevsky, Bull. Math Biophys. 2, pp. 15–25, 65ff. and 109–121 (1940)CrossRefGoogle Scholar
  2. [2]
    A.M. Turing, Phil. Trans. R. Soc. London B 237, 37 (1957)CrossRefGoogle Scholar
  3. [3]
    O.E. Rössler, F.F. Seelig, Z. Naturforsch. 27b, 1444 (1972)Google Scholar
  4. [4a]
    O.E. Rössler, Z. Naturforsch. 31a, 1168 (1976);Google Scholar
  5. [4b]
    C.R. Kennedy, R. Aris, uyen in New Approaches to Nonlinear Problems in Dynamics, P.J. Holmes ed., Philadelphia SIAM, 211 (1980)Google Scholar
  6. [5a]
    O. Sporns, F.F. Seelig, Biosystems 19, 83 and 237 (1986);Google Scholar
  7. [5b]
    O. Sporns, F.F. Seelig, Physica 26D, 215 (1987)Google Scholar
  8. [6]
    B. Röhricht, J. Parisi, J. Peinke, O.E. Rössler, Z. Phys. B Condensed Matter 65, 259 (1986)CrossRefGoogle Scholar
  9. [7a]
    A. Hurwitz, Math. Ann. 46, 273 (1895);CrossRefGoogle Scholar
  10. [7b]
    L. Cesari, Asymptotic Behavior and Stability Problems in ODEs, Springer Verlag, Berlin (1959)Google Scholar
  11. [8]
    C. Grebogi, E. Ott, J.A. Yorke, Physica 7D, 181 (1983)Google Scholar
  12. [9]
    J.M. Thompson, H.B. Stewart, Nonlinear Dynamics and Chaos, Wiley, Chichester (1986)Google Scholar
  13. [10]
    P. Bergé, Y. Pomeau, C. Vidal, Order Within Chaos, Hermann, Paris (1984)Google Scholar
  14. [11]
    O.E. Rössler, J.L. Hudson, M. Klein, Self-similar basin boundaries in a continuos system, in: Nonlinear Dynamics in Engineering, W. Schiehlen, ed., Springer Verlag, Berlin (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • M. Klein
    • 1
  • G. Baier
    • 1
  • O. E. Rössler
    • 1
  1. 1.Department of Theoretical ChemistryUniversity of TübingenTübingenGermany

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