Stability of Nonlinear Systems

  • Frank C. Hoppensteadt
Part of the Applied Mathematical Sciences book series (AMS, volume 94)

Abstract

A mechanical or an electrical device can be constructed to a level of accuracy that is restricted by technical or economic constraints. What happens to the output if the construction is a little off specifications? Does output remain near design values? How sensitive is the design to variations in construction parameters?

Keywords

Nonlinear System Periodic Solution Return Mapping Unstable Manifold Gradient System 
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. 3.1.
    W. Hahn, Stability of Motion, Springer-Verlag, New York, 1967.MATHGoogle Scholar
  2. 3.2.
    E.A. Coddington, N. Levinson, The Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.Google Scholar
  3. 3.3.
    H. Antosiewicz, A survey of Liapunov’s second method, in Contributions to the Theory of Nonlinear Oscillations, S. Lefschetz (ed.), Vol. IV, Princeton, N.J., 1958.Google Scholar
  4. 3.4.
    J.K. Hale, Ordinary Differential Equations, Wiley-Interscience, New York, 1971.Google Scholar
  5. 3.5.
    W.A. Coppel, Stability and Asymptotic Behavior of Differential Equations, Heath, Boston, 1965.MATHGoogle Scholar
  6. 3.6.
    P. Hartmann, Ordinary Differential Equations, Hartmann, Baltimore, 1973.Google Scholar
  7. 3.7.
    J.L. Massera, J.J. Schaffer, Linear Differential Equations and Function Spaces, Academic Press, New York, 1966.MATHGoogle Scholar
  8. 3.8.
    O. Perron, Uber stabilitat und asymptotisches verhalten der Integrale von Differential-gIeichgungenssysteme, Math. Zeit. 29 (1929): 129–160.MathSciNetCrossRefGoogle Scholar
  9. 3.9.
    M. Hirsch, S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, New York, 1974.MATHGoogle Scholar
  10. 3.10
    Preconditioned Conjugate Gradient Methods,Springer-Verlag, New York, 1990.Google Scholar
  11. 3.11
    F.R. Gantmacher, Applications of the Theory of Matrices,Wiley-Interscience, New York, 1959.Google Scholar
  12. 3.12.
    J.L. Massera, Contributions to stability theory, Ann. Math., 64(1956): 182–206; 68 (1958): 202.Google Scholar
  13. 3.13.
    I.G. Malkin, Theorie der Stabilitat einer Bewegung, Oldenbourg, Munich, 1959.Google Scholar
  14. 3.14.
    T. Yoshizawa, Stability Theory and the Existence of Periodic and Almost Periodic Solutions, Springer-Verlag, New York, 1975.MATHCrossRefGoogle Scholar
  15. 3.15.
    F.C. Hoppensteadt, An Introduction to the Mathematics of Neurons, Cambridge University Press, New York, 1986.MATHGoogle Scholar
  16. 3.16.
    A. Denjoy, Sur les courbes definies par les equations differentielles a la surface du tor, J. Math. Pures Appl. 9 (1932): 333–375.Google Scholar
  17. 3.17.
    D.E. Woodward, Phase locking in model neuron networks having group symmetries., Dissertation, University of Utah, 1988.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Frank C. Hoppensteadt
    • 1
  1. 1.College of Natural SciencesMichigan State UniversityEast LansingUSA

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