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Chaotic Behaviours Observed in Homogeneous Chemical Systems

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Synergetics — From Microscopic to Macroscopic Order

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 22))

Abstract

Dynamical systems theory is a branch of mathematical physics, growing rapidly nowadays, which deals with ordinary differential equations and with discrete applications as well. It has introduced into science several new concepts, such as weak stability, strange attractor, mixing of trajectories, and so on. The aim of this lecture is to show how far these ideas prove to be relevant in the study of chemically reacting systems, evolving far from equilibrium. To this end, an overview of the main results obtained over the past four years is presented in what follows. As a conclusion I will mention some still unanswered questions and try to guess how the future could look in this field of experimental research.

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References

  1. C. Vidal, “Chaos and order in Nature” (H. Haken, ed.) Springer-Verlag 1981, p. 69.

    Google Scholar 

  2. C. Vidal, ’Non-linear phenomena in chemical dynamics (C. Vidal, A. Pacault, eds.) Springer-Verlag 1981, p. 49.

    Google Scholar 

  3. W.C. Bray, J. Am. Chem. Soc. 43, 1262 (1921).

    Article  Google Scholar 

  4. B.P. Belousov, “Sb. Ref. Radiat. Med.” Medgiz 1959, p. 145.

    Google Scholar 

  5. It must be reminded that we are dealing with homogeneous reactions. Therefore periodic processes resulting from a competition between a physical effect and a chemical reaction are disregarded: e.g. periodic dissolution of metals in acidic media, periodic decomposition of formaldehyde in concentrated sulphuric acid (Morgan reaction).

    Google Scholar 

  6. A.T. Wilson, M. Calvin, J. Am. Chem. Soc. 77, 5948 (1955).

    Article  Google Scholar 

  7. L.N.M. Duysens, J. Amesz, Biochim. Biophys. Acta, 24, 19 (1957).

    Article  Google Scholar 

  8. J. Chopin-Dumas, P. Richetti, “Non-linear phenomena in chemical dynamics” (C. Vidal, A. Pacault, eds.) Springer-Verlag 1981, p. 213.

    Google Scholar 

  9. J. Boissonade, P. de Kepper, J. Phys. Chem. 84, 501 (1980).

    Article  Google Scholar 

  10. M. Orban, C. Dateo, P. de Kepper, I.R. Epstein, J. Am. Chem. Soc. 104, 1913 (1982).

    Google Scholar 

  11. R.J. Field, E. Körös, R.M. Noyes, J. Am. Chem. Soc. 94, 8649 (1972).

    Article  Google Scholar 

  12. R.J. Field, R.M. Noyes, J. Chem. Phys. 60, 1877 (1974).

    Article  ADS  Google Scholar 

  13. J. Tyson, “The Belousov-Zhabotinsky reaction” Springer-Verlag (1976).

    Google Scholar 

  14. D. Ruelle, Tans. N.Y. Acad. Sci. 35, 66 (1973).

    Google Scholar 

  15. R.A. Schmitz, K.R. Graziani, J.L. Hudson, J. Chem. Phys. 67, 3040 (1977).

    Article  ADS  Google Scholar 

  16. J.L. Hudson, M. Hart, D. Marinko, J. Chem. Phys. 71, 1601 (1979).

    Article  ADS  Google Scholar 

  17. C. Vidal, J.C. Roux, A. Rossi, S. Bachelart, C.R. Acad. Sci. Paris, 289C, 73 (1979)

    Google Scholar 

  18. C. Vidal, J.C. Roux, S. Bachelart, A. Rossi, Ann. N.Y. Acad. Sci. 357, 377 (1980)

    Google Scholar 

  19. D. Ruelle, private communication.

    Google Scholar 

  20. N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Phys. Rev. Lett. 45, 712 (1980).

    Article  ADS  Google Scholar 

  21. J.C. Roux, A. Rossi, S. Bachelart, C. Vidal, Phys. Lett. 77A, 391 (1980).

    Google Scholar 

  22. J.C. Roux, H.L. Swinney, “Non-linear phenomena in chemical dynamics” (C. Vidal, A. Pacault, eds.) Springer-Verlag 1981, p. 38.

    Google Scholar 

  23. J.P. Eckmann, Rev. Mod. Phys. 53, 643 (1981).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Y. Pomeau, P. Manneville, Physica D 1, 219 (1980).

    Google Scholar 

  25. Y. Pomeau, J.C. Roux, A. Rossi, S. Bachelart, C. Vidal, J. Physique Lett. 42, L271 (1981).

    Article  Google Scholar 

  26. R.H. Simonyi, A. Wolf, H.L. Swinney, Phys. Rev. Lett. 49, 245 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  27. N. Metropolis, M.L. Stein, P.R. Stein, J. Comb. Theory, A15, 25 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  28. C. Vidal, S. Bachelart, A. Rossi, J. Physique, 43, 7 (1982).

    Article  Google Scholar 

  29. M. Orban, I.R. Epstein, J. Phys. Chem. 86, 3907 (1982).

    Article  Google Scholar 

  30. P. Gray, J.F. Griffiths, S.M. Hasko, P.G. Lignola, Comb, and Flame, 43, 175 (1980).

    Article  Google Scholar 

  31. K. Tomita, I. Tsuda, Progr. Theor. Phys. 64, 1138 (1980).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. C. Lobry, R. Lozi, “Non-linear phenomena in chemical dynamics” (C. Vidal, A. Pacault, eds.) Springer-Verlag 1981, p. 67.

    Google Scholar 

  33. C. Vidal, A. Rossi, “Non-linear phenomena in chemical dynamics” (C. Vidal, A. Pacault, eds.) Springer-Verlag 1981, p. 277.

    Google Scholar 

  34. M. Dubois, private communication.

    Google Scholar 

  35. H.S. Greenside, A. Wolf, J. Swift, T. Pignataro, Phys. Rev. A, 25, 3453 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  36. J.C. Roux, R.H. Simonyi, H.L. Swinney, Physica D, in press.

    Google Scholar 

  37. J.D. Farmer, Physica D, 4, 366 (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. A. Lafon, A. Rossi, C. Vidal, J. Physique, 44, 505 (1983).

    Article  Google Scholar 

  39. G. Nicolis, I. Prigogine,“Self-organization in non-equilibrium systems”, Wiley & Sons (1977).

    Google Scholar 

  40. W. Horstemke, R. Lefever, “Noise induced transitions” Springer-Verlag, 1983.

    Google Scholar 

  41. J.D. Farmer, private communication.

    Google Scholar 

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© 1984 Springer-Verlag Berlin Heidelberg

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Vidal, C. (1984). Chaotic Behaviours Observed in Homogeneous Chemical Systems. In: Frehland, E. (eds) Synergetics — From Microscopic to Macroscopic Order. Springer Series in Synergetics, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69540-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-69540-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-69542-1

  • Online ISBN: 978-3-642-69540-7

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