Stability Analysis for Discrete Biological Models Using Algebraic Methods

Xiaoliang Li (1) , Chenqi Mou (2) , Wei Niu (2) , Dongming Wang (2)

1 BUAA - Beihang University
2 SALSA - Solvers for Algebraic Systems and Applications

This paper is concerned with stability analysis of biological networks modeled as discrete and finite dynamical systems. We show how to use algebraic methods based on quantifier elimination, real solution classification and discriminant varieties to detect steady states and to analyze their stability and bifurcations for discrete dynamical systems. For finite dynamical systems, methods based on Gröbner bases and triangular sets are applied to detect steady states. The feasibility of our approach is demonstrated by the analysis of stability and bifurcations of several discrete biological models using implementations of algebraic methods.

Mots clés: Symbolic computation; Algebraic method; Bifurcation; Finite dynamical system; Stability; Discrete dynamical system

Domaines: Informatique [cs]

Xiaoliang Li, Chenqi Mou, Wei Niu, Dongming Wang. Stability Analysis for Discrete Biological Models Using Algebraic Methods. The Joint Conference of ASCM 2009 and MACIS 2009, Dec 2009, Fukuoka, Japan. pp.382-385. ⟨hal-01294709⟩