On Muldowney’s Criteria for Polynomial Vector Fields with Constraints

  • Hassan Errami
  • Werner M. Seiler
  • Thomas Sturm
  • Andreas Weber
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6885)


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.


Periodic Orbit Polynomial Vector Elimination Problem Cylindrical Algebraic Decomposition Dulac Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hassan Errami
    • 1
  • Werner M. Seiler
    • 2
  • Thomas Sturm
    • 3
  • Andreas Weber
    • 1
  1. 1.Institut für Informatik IIUniversität BonnBonnGermany
  2. 2.Institut für MathematikUniversität KasselKasselGermany
  3. 3.Max-Planck-Institut für Informatik , RG 1: Automation of LogicSaarbrückenGermany

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