Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology

Authors:
Thomas Sturm;Andreas Weber
Affiliations:
Universität Passau, Passau, Germany 94030;Institut für Informatik II, Universität Bonn, Bonn, Germany 53117
Venue:
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Year:
2008

Citing 9
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Abstract

Symbolic methods for investigating Hopf bifurcation problems of vector fields arising in the context of algebraic biology have recently obtained renewed attention. However, the symbolic investigations have not been fully algorithmic but required a sequence of symbolic computations intervened with ad hoc insights and decisions made by a human. In this paper we discuss the use of generic methods to reduce questions on the existence of Hopf bifurcations in parameterized polynomial vector fields to quantifier elimination problems over the reals combined with simplification techniques available in REDLOG. We can reconstruct most of the results given in the literature within a few seconds of computation time. As no tedious hand computations are involved we presume that the use of these generic methods will be a useful tool for investigating other examples.