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On Muldowney’s Criteria for Polynomial Vector Fields with Constraints

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Computer Algebra in Scientific Computing (CASC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6885))

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Abstract

We study Muldowney’s extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields. Using the formulation of Muldowney’s sufficient criteria for excluding periodic orbits of the parameterized vector field on a convex set as a quantifier elimination problem over the ordered field of the reals we provide case studies of some systems arising in the life sciences. We discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney’s criteria.

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Author information

Authors and Affiliations

  1. Institut für Informatik II, Universität Bonn, Friedrich-Ebert-Allee 144, 53113, Bonn, Germany

    Hassan Errami & Andreas Weber

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Werner M. Seiler

  3. Max-Planck-Institut für Informatik , RG 1: Automation of Logic, 66123, Saarbrücken, Germany

    Thomas Sturm

Authors
  1. Hassan Errami
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  2. Werner M. Seiler
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  3. Thomas Sturm
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  4. Andreas Weber
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Editor information

Editors and Affiliations

  1. Laboratory of Information Technologies (LIT), Joint Institute for Nuclear Research (JINR), 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Institut für Informatik, Lehrstuhl für Effiziente Algorithmen, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Ernst W. Mayr

  4. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Evgenii V. Vorozhtsov

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© 2011 Springer-Verlag Berlin Heidelberg

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Errami, H., Seiler, W.M., Sturm, T., Weber, A. (2011). On Muldowney’s Criteria for Polynomial Vector Fields with Constraints. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2011. Lecture Notes in Computer Science, vol 6885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23568-9_11

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  • DOI: https://doi.org/10.1007/978-3-642-23568-9_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23567-2

  • Online ISBN: 978-3-642-23568-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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