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Relaxation oscillations including a standard chase on French ducks

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 985))

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References

  • E. Benoit, J.L. Callot, F. Diener, M. Diener, "Chasse au Canard". IRMA*, Strasbourg (1980).

    MATH  Google Scholar 

  • G.F. Carrier, J.A. Lewis, "The relaxation oscillations of the Van der Pol oscillator". Advanc. Appl. Mech. Vol. 3, Academic Press (1953), p.12–16.

    Google Scholar 

  • F. Diener, "Les Canards de l’équation ÿ+(ẏ+a)2+y=0". IRMA, Strasbourg (1980)

    Google Scholar 

  • M. Diener, "Étude générique des canards", IRMA, Strasburg (1981)

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  • W. Eckhaus, "New approach to the asymptotic theory of non-linear oscillations". Journ. Math. Anal. & Appl. Vol.49 (1975), p. 575–611.

    Article  MathSciNet  MATH  Google Scholar 

  • W. Eckhaus, "Asymptotic analysis of singular perturbations". North-Holland (1979)

    Google Scholar 

  • A. Liénard, "Étude des oscillations entrenues", Revue Générale de l’électricite (1928) p. 901.

    Google Scholar 

  • A.H. Lightstone, A. Robinson, "Non-archimedean fields and asymptotic expansions", North Holland (1975).

    Google Scholar 

  • R. Lutz, M. Goze, "Non-standard analysis. A practical quide with applications". Springer Lecture Notes in Math. 881 (1981).

    Google Scholar 

  • E.F. Mishchenko, N.Kh. Rozov, "Differential equations with small parameters and relaxation oscillations". PlenumPress (1980), Original Russian edition (1975).

    Google Scholar 

  • B. van der Pol, "A theory of the amplitude of free and forced triode vibrations", Radio Review (1920).

    Google Scholar 

  • B. van der Pol, "On relaxation oscillations". Phil. Mag.2 (1927), p.978.

    Google Scholar 

  • A. Robinson, "Non standard analysis, North-Holland (1966).

    Google Scholar 

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F. Verhulst

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© 1983 Springer-Verlag

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Eckhaus, W. (1983). Relaxation oscillations including a standard chase on French ducks. In: Verhulst, F. (eds) Asymptotic Analysis II —. Lecture Notes in Mathematics, vol 985. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062381

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  • DOI: https://doi.org/10.1007/BFb0062381

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12286-9

  • Online ISBN: 978-3-540-39612-3

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