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Qualitative Reasoning and Bifurcations in Dynamic Systems

  • Juan J. Flores
  • Andrzej Proskurowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4293)

Abstract

A bifurcation occurs in a dynamic system when the structure of the system itself and therefore also its qualitative behavior change as a result of changes in one of the system’s parameters. In most cases, an infinitesimal change in one of the parameters make the dynamic system exhibit dramatic changes. In this paper, we present a framework (QRBD) for performing qualitative analysis of dynamic systems exhibiting bifurcations. QRBD performs a simulation of the system with bifurcations, in the presence of perturbations, producing accounts for all events in the system, given a qualitative description of the changes it undergoes. In such a sequence of events, we include catastrophic changes due to perturbations and bifurcations, and hysteresis. QRBD currently works with first-order systems with only one varying parameter. We propose the qualitative representations and algorithm that enable us to reason about the changes a dynamic system undergoes when exhibiting bifurcations, in the presence of perturbations.

Keywords

Phase Portrait Bifurcation Diagram Bifurcation Point Qualitative Description Simulation Algorithm 
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.
    Kuipers, B.J.: Qualitative simulation. Artificial Intelligence 29, 289–338 (1986)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Forbus, K.D.: Qualitative process theory. Artificial Intelligence 24, 85–168 (1984)CrossRefGoogle Scholar
  3. 3.
    de Kleer, J., Brown, J.S.: Qualitative physics based on confluences. Artificial Intelligence 24, 7–83 (1984)CrossRefGoogle Scholar
  4. 4.
    Lee, W.W., Kuipers, B.J.: A qualitative method to construct phase portraits. In: Proc.11th National Conf.on Artificial Intelligence (AAAI 1993), pp. 614–619. AAAI Press/The MIT Press, Menlo Park, Cambridge, London (1993)Google Scholar
  5. 5.
    Strogatz, S.H.: Nonlinear Dynamics and Chaos with Applications to Physics, Biology, and Engineering. Westview Press, Cambridge, MA (1994)Google Scholar
  6. 6.
    Keller, H.B.: Numerical methods in bifurcation problems. Springer, Heidelberg (1987)MATHGoogle Scholar
  7. 7.
    Kuipers, B.J.: Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge. MIT Press, Cambridge (1994)Google Scholar
  8. 8.
    Wolfram, S.: The Mathematica Book. Cambridge University Press, Cambridge (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Juan J. Flores
    • 1
  • Andrzej Proskurowski
    • 2
  1. 1.Division de Estudios de Postgrado, Facultad de Ingenieria ElectricaUniversidad MichoacanaMoreliaMexico
  2. 2.Computer Science DepartmentUniversity of OregonEugeneUSA

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