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Erschienen in:
2011 | OriginalPaper | Buchkapitel
On Muldowney’s Criteria for Polynomial Vector Fields with Constraints
verfasst von : Hassan Errami, Werner M. Seiler, Thomas Sturm, Andreas Weber
Erschienen in: Computer Algebra in Scientific Computing
Verlag: Springer Berlin Heidelberg
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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.