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Qualitative Reasoning and Bifurcations in Dynamic Systems

  • Conference paper
MICAI 2006: Advances in Artificial Intelligence (MICAI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4293))

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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.

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Author information

Authors and Affiliations

  1. Division de Estudios de Postgrado, Facultad de Ingenieria Electrica, Universidad Michoacana, Morelia, Mexico

    Juan J. Flores

  2. Computer Science Department, University of Oregon, Eugene, OR, USA

    Andrzej Proskurowski

Authors
  1. Juan J. Flores
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  2. Andrzej Proskurowski
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Editor information

Editors and Affiliations

  1. Center for Computing Research, National Polytechnic Institute, 07738, Mexico City, México

    Alexander Gelbukh

  2. Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE), Luis Enrique Erro No. 1, Sta. Ma. Tonanzintla, 72840, Puebla, México

    Carlos Alberto Reyes-Garcia

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© 2006 Springer-Verlag Berlin Heidelberg

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Flores, J.J., Proskurowski, A. (2006). Qualitative Reasoning and Bifurcations in Dynamic Systems. In: Gelbukh, A., Reyes-Garcia, C.A. (eds) MICAI 2006: Advances in Artificial Intelligence. MICAI 2006. Lecture Notes in Computer Science(), vol 4293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11925231_25

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  • DOI: https://doi.org/10.1007/11925231_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-49026-5

  • Online ISBN: 978-3-540-49058-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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