Skip to main content
SpringerLink
Log in

Etude macroscopique de l'equation de van der Pol

  • Part I: Theory of Singular Perturbations
  • Conference paper
  • First Online:
Theory and Applications of Singular Perturbations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 942))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. R. BELLMAN: On the boundedness of solutions of nonlinear differential and difference equations. Trans. Amer. Math. Soc. 62, 357–386 (1947).

    Article  MathSciNet  MATH  Google Scholar 

  2. F. BRAUER, J.A. NOHEL: Qualitative theory of ordinary differential equations. W.A. Benjamin, Inc., New-York-Amsterdam (1969).

    MATH  Google Scholar 

  3. M.L. CARTWRIGHT:— Forced oscillations in non-linear systems. Contributions to the theory of nonlinear oscillations 149–241. Princeton University Press. 1950 (Annals of Math. Studies No. 20. —Van der Pol's equation for relaxation oscillations. Vol. 2. Princeton University Press (1952). Annals of Math. Studies No. 29.

    Google Scholar 

  4. A.D. DRAGILEV: Periodic solutions of the differential equation of nonlinear oscillations (Russian), Prik. Math. i Meh. 16 (1949) 85–89.

    MathSciNet  Google Scholar 

  5. D. GRAFFI: Forced oscillations for several nonlinear circuits. Annals of Math. (2) 54:262–271 (1951).

    Article  MathSciNet  MATH  Google Scholar 

  6. C. HAYASHI: Forced oscillations in nonlinear systems. Osaka Nippon printing and publ. Co. (1953).

    Google Scholar 

  7. S. LEFSCHETZ: Differential equations. Geometric theory. Interscience Publishers John Wiley and Sons, New-York, London.

    Google Scholar 

  8. N. LEVINSON: On the existence of periodic solutions for second order differential equation with a forcing term. Jour. of Math. and Phys. 22, 41–48 (1949).

    Article  MathSciNet  MATH  Google Scholar 

  9. N. LEVINSON, O.K. SMITH: A general equation for relaxation oscillations. Duke Math. Jour. 9, 382–403 (1942).

    Article  MathSciNet  MATH  Google Scholar 

  10. A. LIENARD: Etude des oscillations entretenues. Revue générale de l'Electricité 23, 901–912, 946–954 (1928).

    Google Scholar 

  11. S. MISOHATA, M. YAMAGUTI: On the existence of periodic solutions of the nonlinear differential equations x″+a(x)x′+(x)=p(t). Memoirs College of Science Univ. of Kyoto, Seria A Mathematics 27, 109–113 (1952).

    MATH  Google Scholar 

  12. V.V. NEMITSKI, V.V. STEPANOV: Qualitative theory of differential equations. Princeton University Press (1960).

    Google Scholar 

  13. H. POINCARE: Mémoire sur les courbes définies par une équation différentielle Jour. Math. Pures et Appl. (3). Ouvres t. 1.

    Google Scholar 

  14. B. VAN DER POL: On oscillations hystérésis in a triodgenerator with two degrees of freedom. Phil. Mag. (6) 43, 700–709 (1922).

    Google Scholar 

  15. B. VAN DER POL: On relaxations oscillations. Phil. Mag. (7) 2, 978–992 (1926).

    Google Scholar 

  16. G.E.H. REUTER: A boundedness theorem for non-linear differential equations of the second order. I. Proc. Cambridge Phil. Soc. 47, 49–54 (1951). II. Journal London Math. Soc. 27, 48–58 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  17. E. BENOIT: Equation de van der Pol avec 20 terme forcant. Thèse 30 sycle. Publication IRMA. Strasborg No. 45 (1979).

    Google Scholar 

  18. J.L. CALLOT: Bifurcation du portrait de phase pour des équations différentielles du second ordre. Thèse Strasbourg (1981).

    Google Scholar 

  19. F. DIENER: Méthode du plan, d'observabilité. Thèse Strasbourg (1981).

    Google Scholar 

  20. M. DIENER: Etude générique des canards. Thèse Strasbourg (1981).

    Google Scholar 

  21. R. LUTZ, T. SARI: Sur le comportement asymptotique des solutions dans un problème non linéaire. C.R. Acad. Sc. Paris 292 (1981).

    Google Scholar 

  22. T. SARI: Sur le comportement asymptotique des solutions dans un problème aux limites semi-linéaire. C.R. Acad. Sc. Paris 292 (1981).

    Google Scholar 

  23. A. TROESCH: Etude qualitative de systèmes différentiels: une approche basée sur l'analyse non standard. Thèse Strasbourg (1981).

    Google Scholar 

  24. A. TROESCH, E. URLACHER: Analyse non standard et équation de van der Pol. Séries de Math. Pures et Appliquées I.R.M.A. (1976–77) 11/P-04, 1–21.

    Google Scholar 

  25. A. TROESCH, E. URLACHER: Perturbations singulières et Analyse non standard. Ck-convergence et crépitement. Séries de Math. Pures et Appliquées I.R.M.A. (1976–77) 11/P-04, 21–47.

    Google Scholar 

  26. A. TROESCH, E. URLACHER: Perturbations singulières et analyse non classique. C.R. Acad. Sc. 286 (1978).

    Google Scholar 

  27. A. TROESCH, E. URLACHER: Perturbations singulières et analyse non standard. C.R. Acad. Sc. 287 (1978).

    Google Scholar 

  28. E. URLACHER: Oscillations de relaxations et analyse non standard. Thèse Strasbourg (1981).

    Google Scholar 

  29. P. CARTIER: Perturbations singulières des équations différentielles ordinaires et Analyse non standard. Séminaire Bourbaki No. 580 (Novembre 1981).

    Google Scholar 

  30. BOBO SEKE: Ombres des graphes de fonctions continues. Thèse Strasbourg (1981).

    Google Scholar 

  31. J. HARTONG: Vision macroscopique de phénomènes périodiques. Thèse Strasbourg (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut de Recherche Mathematique Avancee Laboratoire Associé au C.N.R.S. no 1, Université Louis Pasteur, 7, Rue René Descartes, 67084, Strasbourg Cédex

    Albert Troesch

Authors
  1. Albert Troesch
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

W. Eckhaus E. M. de Jager

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Troesch, A. (1982). Etude macroscopique de l'equation de van der Pol. In: Eckhaus, W., de Jager, E.M. (eds) Theory and Applications of Singular Perturbations. Lecture Notes in Mathematics, vol 942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094744

Download citation

  • DOI: https://doi.org/10.1007/BFb0094744

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11584-7

  • Online ISBN: 978-3-540-39332-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation