Mathematics in Computer Science

, Volume 1, Issue 3, pp 507–539 | Cite as

Algebraic Approaches to Stability Analysis of Biological Systems

Article

Abstract.

In this paper, we improve and extend the approach of Wang and Xia for stability analysis of biological systems by making use of Gröbner bases, (CAD-based) quantifier elimination, and discriminant varieties, as well as the stability criterion of Liénard and Chipart, and showing how to analyze the stability of Hopf bifurcation points. The stability and bifurcations for a class of self-assembling micelle systems with chemical sinks are analyzed in detail. We provide experimental results with comparisons for 15 biological models taken from the literature.

Mathematics Subject Classification (2000).

Primary 34D20 Secondary 68W30 Tertiary 78A70 

Keywords.

Bifurcation biological model CAD discriminant variety equilibrium Gröbner basis quantifier elimination real solution classification stability steady state self-assembling micelle system triangular decomposition 

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Copyright information

© Springer 2008

Authors and Affiliations

  1. 1.Laboratoire d’Informatique de Paris 6Université Pierre et Marie Curie – CNRSParisFrance
  2. 2.LMIB – School of ScienceBeihang UniversityBeijingChina

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