Algebraic approaches to stability analysis of biological systems

Wei Niu (1) , Dongming Wang (1)

1 SALSA - Solvers for Algebraic Systems and Applications

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.

Domaines: Systèmes dynamiques [math.DS]; Calcul formel [cs.SC]

Wei Niu, Dongming Wang. Algebraic approaches to stability analysis of biological systems. Mathematics in Computer Science, 2008, 1 (3), pp.507-539. ⟨10.1007/s11786-007-0039-x⟩. ⟨hal-00588726⟩