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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.
