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Journal Article

Algorithmic Global Criteria for Excluding Oscillations

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons73108

Sturm,  Thomas
Automation of Logic, MPI for Informatics, Max Planck Society;

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Citation

Weber, A., Sturm, T., & Abdel-Rahman, E. O. (2011). Algorithmic Global Criteria for Excluding Oscillations. Bulletin of Mathematical Biology, 73(4), 899-916. doi:10.1007/s11538-010-9618-0.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0010-14E2-A
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.