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Synergetics pp 105-145 | Cite as

Necessity

Old Structures Give Way to New Structures
  • Hermann Haken
Chapter
  • 106 Downloads

Abstract

This chapter deals with completely deterministic processes. The question of stability of motion plays a central role. When certain parameters change, stable motion may become unstable and completely new types of motion (or structures) appear. Though many of the concepts are derived from mechanics, they apply to many disciplines.

Keywords

Singular Point Static Instability Excited Atom Stable Limit Cycle Potential Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. N. N. Bogoliubov, Y. A. Mitropolsky: Asymptotic Methods in the Theory of Nonlinear Oscillations (Hindustan Publ. Corp., Delhi 1961)Google Scholar
  2. N. Minorski: Nonlinear Oscillations (Van Nostrand, Toronto 1962)Google Scholar
  3. A. Andronov, A. Vitt, S. E. Khaikin: Theory of Oscillators (Pergamon Press, London-Paris 1966)zbMATHGoogle Scholar
  4. D. H. Sattinger In Lecture Notes in Mathematics, Vol. 309: Topics in Stability and Bifurcation Theory, ed. by A. Dold, B. Eckmann (Springer, Berlin-Heidelberg-New York 1973)Google Scholar
  5. M. W. Hirsch, S. Smale: Differential Equations, Dynamical Systems, and Linear Algebra (Academic Press, New York-London 1974)zbMATHGoogle Scholar
  6. V. V. Nemytskii, V. V. Stepanov: Qualitative Theory of Differential Equations (Princeton Univ. Press, Princeton, N.J. 1960)zbMATHGoogle Scholar
  7. H. Poincaré: Oeuvres, Vol. 1 (Gauthiers-Villars, Paris 1928)Google Scholar
  8. H. Poincaré: Sur l’equilibre d’une masse fluide animée d’un mouvement de rotation. Acta Math. 7 (1885)Google Scholar
  9. H. Poincaré: Figures d’equilibre d’une masse fluide (Paris 1903)Google Scholar
  10. H. Poincaré: Sur le problème de trois corps et les équations de la dynamique. Acta Math. 13 (1890)Google Scholar
  11. H. Poincaré: Les méthodes nouvelles de la méchanique céleste (Gauthier-Villars, Paris 1892–1899)Google Scholar
  12. J. La Salle, S. Lefshetz: Stability by Ljapunov’s Direct Method with Applications (Academic Press, New York-London 1961)Google Scholar
  13. W. Hahn: Stability of Motion. In Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Bd. 138 (Springer, Berlin-Heidelberg-New York 1967)Google Scholar
  14. F. Schlögl: Z. Phys. 243, 303 (1973)Google Scholar
  15. A. Lotka: Proc. Nat. Acad. Sci. (Wash.) 6, 410 (1920)ADSCrossRefGoogle Scholar
  16. V. Volterra: Leçons sur la théorie mathematiques de la lutte pour la vie (Paris 1931)Google Scholar
  17. N. S. Goel, S. C. Maitra, E. W. Montroll: Rev. Mod. Phys. 43,231 (1971)MathSciNetADSCrossRefGoogle Scholar
  18. B. van der Pol: Phil. Mag. 43, 6, 700 (1922); 2, 7, 978 (1926); 3, 7, 65 (1927)Google Scholar
  19. H. T. Davis: Introduction to Nonlinear Differential and Integral Equations (Dover Publ. Inc., New York 1962)zbMATHGoogle Scholar
  20. R. Thom: Structural Stability and Morphogenesis (W. A. Benjamin, Reading, Mass. 1975)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Hermann Haken
    • 1
  1. 1.Institut für Theoretische PhysikUniversität StuttgartStuttgart 80Germany

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