Algorithmic global criteria for excluding oscillations
In: Bulletin of Mathematical Biology (Apr. 2011), 73:4(899-917)
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.
Bibtex
@ARTICLE{WeberSturm2010a, author = {Weber, Andreas and Sturm, Thomas and Abdel-Rahman, Essam O.}, pages = {899--917}, title = {Algorithmic global criteria for excluding oscillations}, journal = {Bulletin of Mathematical Biology}, volume = {73}, number = {4}, year = {2011}, month = apr, note = {Special issue on ``Algebraic Biology''.}, 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.}, doi = {10.1007/s11538-010-9618-0} }