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Investigating Generic Methods to Solve Hopf Bifurcation Problems in Algebraic Biology

  • Thomas Sturm
  • Andreas Weber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5147)

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.

Keywords

Hopf Bifurcation Symbolic Computation Atomic Formula Bifurcation Problem Existential Closure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Thomas Sturm
    • 1
  • Andreas Weber
    • 2
  1. 1.Universität PassauPassauGermany
  2. 2.Institut für Informatik IIUniversität BonnBonnGermany

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