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Existence Criteria for Bifurcations as Stability Criteria for Critical Nonlinear Control Systems

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Theoretical Approaches to Complex Systems

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 21))

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Abstract

Critical systems are defined as systems whose stability behavior cannot be decided in first approximation.The linear part of the corresponding operator has at least one eigenvalue with vanishing real part and the rest with negative real parts.

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References

  1. N. N. Bautin, Das Verhalten dynamischer Systeme an den Grenzen des Stabilitätsbereichs, Moskau (1950), (russ.).

    Google Scholar 

  2. W. Forrester, World Dynamics, Cambridge, Wright-Allen Press (1971).

    Google Scholar 

  3. H. Hahn, Zur Diskrepanz zwischen Theorie und Praxis nichtlinearer Regelkreise, Preprint Universität Tübingen (1975).

    Google Scholar 

  4. H. Hahn, Zum Problem der praktischen Stabilität, Berichte der Mathematisch-Statistischen Sektion im Forschungszentrum Graz, (1976).

    Google Scholar 

  5. H. Hahn, The application of root-locus-technique to nonlinear control systems with multiple steady states, Intern. J. of Control, (1977).

    Google Scholar 

  6. H. Hahn, Theorie und Anwendung des “Newton-Diagramms” bei nichtlinearen Regelsystemen, Preprint Universität Tübingen, (1976).

    Google Scholar 

  7. W. Hahn, Stability of Motion, Springer Verlag, (1967).

    MATH  Google Scholar 

  8. J. Hale, J. Diff. Eq. 10 (1971),PP.59 – 82.

    Article  MATH  MathSciNet  Google Scholar 

  9. R. Hausrath , J. Diff. Eq. 13 (1973), pp. 329 – 357.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Kelly, J. Math. Anal. Appl. (1967), pp. 336 – 344.

    Google Scholar 

  11. J.E. Marsden, M. Mc Cracken, The Hopf Bifurcation and its Application, Springer (1976).

    Book  Google Scholar 

  12. D. Meadows et al, The Limits to Growth, Universe Books, (1972).

    Google Scholar 

  13. M. Mesarovic, E. Pestel, A Goal-seeking and Regionalized Model for Analysis of Critical World-Relationship — A Conceptional Foundation, Kybernetes , (1972).

    Google Scholar 

  14. W. Reissig, G. Sansone, R. Conti, Nichtlineare Differentialgleichungen höherer Ordnung, Cremonese, (1969).

    MATH  Google Scholar 

  15. M.M. Vainberg, V. A. Trenogin, Theory of branching of solutions of nonlinear equations, Noordhoff, (1974).

    Google Scholar 

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© 1978 Springer-Verlag Berlin Heidelberg

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Hahn, H. (1978). Existence Criteria for Bifurcations as Stability Criteria for Critical Nonlinear Control Systems. In: Heim, R., Palm, G. (eds) Theoretical Approaches to Complex Systems. Lecture Notes in Biomathematics, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93083-6_2

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  • DOI: https://doi.org/10.1007/978-3-642-93083-6_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08757-1

  • Online ISBN: 978-3-642-93083-6

  • eBook Packages: Springer Book Archive

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