Algebraic Approaches to Stability Analysis of Biological Systems

Algebraic Approaches to Stability Analysis of Biological Systems

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 ...

Algebraic Analysis of Stability for Some Biological Systems

This paper presents some results about the stability of certain biological systems, including the Cinquin–Demongeot model of multistable switch, self-assembling micelle systems, and the Cdc2cyclin B/Wee1 system. The results are obtained and rigorously proved by means of real solving and solution classification using symbolic computation.

Multiobjective approaches to the data driven analysis of biological systems

Stability Analysis for Discrete Biological Models Using Algebraic Methods

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...

Algebraic Analysis of Bifurcation and Limit Cycles for Biological Systems

In this paper, we show how to analyze bifurcation and limit cycles for biological systems by using an algebraic approach based on triangular decomposition, Gröbner bases, discriminant varieties, real solution classification, and quantifier elimination by partial CAD. The analysis of bifurcation and limit cycles for a concrete two-dimensional system, the self-assembling micelle system with chemi...