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Chaos and Order in Nature pp 92–101Cite as

Dispersive Instabilities in Nonlinear Systems: The Real and Complex Lorenz Equation

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Part of the book series: Springer Series in Synergetics ((SSSYN,volume 11))

Abstract

The main aim of this article is to consider, in the weakly nonlinear sense, the evolution of systems which become unstable as a parameter (μ) is varied but in which the instability is caused not by dissipation but by dispersive effects. We use the method first developed by STUART [1] in hydrodynamic stability to consider the development of waves at the critical or bifurcation point.

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References

  1. J.T. Stuart, J. Fluid Mech, 9, 353, 1960.

    Article  Google Scholar 

  2. J.D. Gibbon and M.J. McGuinness, Proc. Roy. Soc. London A 377A, Issue 1769, 1981.

    Google Scholar 

  3. M. Weissman, Phil. Trans. Royal. Soc. Lond, 290, 639, 1979.

    Google Scholar 

  4. C. Lange and A.C., Newell, SIAM Jour. Appl. Math, 21, 605, 1971.

    Article  Google Scholar 

  5. J.D. Gibbon, I.N. James, and I.M. Moroz, Proc. Royal. Soc. London, A367, 219, 1979.

    Article  Google Scholar 

  6. A.C. Newell and J.A. Whitehead: J. Fluid Mech, 38, 279, 1969. A.C. Newell: Nonlinear Wave Motion (ed. A.C. Newell), Vol. 15, AMS., Providence, Rhode Island 1974.

    Article  Google Scholar 

  7. K. Stewartson and J.T. Stuart: J. Fluid Mech, 48, 529, 1971.

    Article  Google Scholar 

  8. G.L. Lamb: Rev. Mod. Phys, 43, 99, 1971.

    Article  CAS  Google Scholar 

  9. J. Pedlosky: J. Atmos. Sci, 79, 680, 1972.

    Article  Google Scholar 

  10. I.M. Moroz: J. Atmos. Sci., to appear 1981.

    Google Scholar 

  11. J.D. Gibbon and M.J. McGuinness: Phys. Letts, 77A, 295, 1980.

    Article  Google Scholar 

  12. J.D. Gibbon and M.J. McGuinness: Preprint 1980, Submitted to Physica D.

    Google Scholar 

  13. J. Pedlosky: J. Atmos. Sci, 28, 587, 1980.

    Article  Google Scholar 

  14. J. Pedlosky & C. Frenzen: J. Itmos. Sci, 37, 1177, 1980.

    Article  Google Scholar 

  15. J. Brindley & I.M. Moroz: Phys. Letts, 77A 441, 1980. Also preprint University of Leeds, Maths. Dept. 1981

    Article  Google Scholar 

  16. H. Haken: Phys. Letts, 53A, 77, 1975, also Synergetics; An Introduction, 2nd ed. Springer Series in Synergetics, Vol. 1 (Springer Berlin, Heidelberg, New York 1978 )

    Article  Google Scholar 

  17. E.N. Lorenz: J. Atmos. Sci, 20, 130, 1963.

    Article  Google Scholar 

  18. A.C. Fowler, J.D. Gibbon & MT. McGuinness: The Complex Lorenz equations; preprint 1981 M.I.T. Maths. Department: Submitted to Physica D.

    Google Scholar 

  19. J.B. McLaughlin & P.C. Martin: Phys. Rev 12A, 186, 1975.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Imperial College of Science and Technology, London, SW7 2BZ, Great Britain

    J. D. Gibbon

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  1. J. D. Gibbon
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Editors and Affiliations

  1. Institut für Theoretische Physik, Universitä Stuttgart, Pfaffenwaldring 57/IV, D-7000, Stuttgart 80, Fed. Rep. of Germany

    Hermann Haken

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Gibbon, J.D. (1981). Dispersive Instabilities in Nonlinear Systems: The Real and Complex Lorenz Equation. In: Haken, H. (eds) Chaos and Order in Nature. Springer Series in Synergetics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-68304-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-68304-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-68306-0

  • Online ISBN: 978-3-642-68304-6

  • eBook Packages: Springer Book Archive

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