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Computer Algebra Programs for Dynamical Systems Theory

  • D. Armbruster
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 37)

Abstract

This is a description of the current state of that part of the program outlined in [1], that is concerned with the development of Computer Algebra tools for the analysis of dynamical systems. At the moment there is only one program generally accessible (i.e. published) which fits into this context. It deals with nonlinear near identity transformations [4] and can thus be used to determine center manifolds and normal forms. We present here two additional programs in MACSYMA which do averaging for nonautonomous o.d.e’s and which do a Lyapunov — Schmidt reduction for a steady state bifurcation, respectively. Further programs implementing various perturbation methods, Lie-series and a more general Lyapunov — Schmidt reduction which allows to treat some classes of p.d.e’s will be published in [3].

Keywords

Center Manifold Bifurcation Parameter Order Average Dynamical System Theory Identity Transformation 
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. 1.
    Armbruster, D.: (1985) Bifurcation theory and computer algebra: an initial approach. In: (Caviness, B.F., ed.) Proceedings of EUROCAL 85 Vol II, Springer Lec. Notes Comp. Sci. 204, 126–137.Google Scholar
  2. 2.
    Golubitsky, M., Sehaeffer, D.: (1985) Singularities and groups in bifurcation theory I, SpringerzbMATHGoogle Scholar
  3. 3.
    Rand, R.H., Armbruster, D.: Perturbation Methods, bifurcation theory, and computer algebra, Springer to appear 1987zbMATHCrossRefGoogle Scholar
  4. 4.
    Rand, R.H., Keith, W.L.: 1985 Normal form and center manifold calculations on MACSYMA. In: (Pavelle, R. ed.) Applications of computer algebra, Kluwer, 309–328.Google Scholar
  5. 5.
    Sanders, J.A., Verhulst,F.: (1985) Averaging methods in nonlinear dynamical systems, SpringerzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • D. Armbruster
    • 1
    • 2
  1. 1.Mathematical Sciences InstituteCornell UniversityIthacaUSA
  2. 2.Institut für InformationsverarbeitungUniversität TübingenTübingenFed.Rep.of Germany

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