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Algorithmic Global Criteria for Excluding Oscillations

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Abstract

We investigate algorithmic methods to tackle the following problem: Given a system of parametric ordinary differential equations built by a biological model, does there exist ranges of values for the model parameters and variables which are both meaningful from a biological point of view and where oscillating trajectories, can be found? We show that in the common case of polynomial vector fields known criteria excluding the existence of non-constant limit cycles lead to quantifier elimination problems over the reals.

We apply these criteria to various models that have been previously investigated in the context of algebraic biology.

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Authors and Affiliations

  1. Institut für Informatik II, Universität Bonn, Römerstr. 164, 53117, Bonn, Germany

    Andreas Weber & Essam O. Abdel-Rahman

  2. Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071, Santander, Spain

    Thomas Sturm

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  1. Andreas Weber
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Correspondence to Andreas Weber.

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Weber, A., Sturm, T. & Abdel-Rahman, E.O. Algorithmic Global Criteria for Excluding Oscillations. Bull Math Biol 73, 899–916 (2011). https://doi.org/10.1007/s11538-010-9618-0

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