PhD graduated
Team : SALSA
Departure date : 08/31/2011

Supervision : Dongming WANG

Qualitative Analysis of Biological Systems Using Algebraic Methods

This thesis is dedicated to qualitative analysis of biological systems, modeled as systems of differential or difference equations, using algebraic methods. We study the problems of detecting steady states, analyzing stability and different kinds of bifurcations, and constructing limit cycles for both continuous and discrete biological models, show how to reduce these problems to those of solving polynomial or semi-algebraic systems according to stability criteria and techniques from the qualitative theory of dynamical systems, and explain how the latter problems can be solved by using an algebraic approach based on the methods of triangular sets, Gröbner bases, quantifier elimination, and real solution isolation and classification. Experiments with various biological systems show the effectiveness of our algebraic approach. In particular, the stability, three kinds of bifurcations, and limit cycles for the self-assembling micelle system with chemical sinks are successfully analyzed. Exact algebraic conditions on the parameters of this system are derived to describe the kinds of bifurcations and the stability and types of the bifurcation points, and three limit cycles are constructed from a steady state by small perturbation.

Defence : 06/17/2011

Jury members :

M. François Boulier, Professeur, Université Lille I [Rapporteur]
M. Bican Xia, Professor, Peking University [Rapporteur]
M. Jean-Charles Faugère, Directeur de Recherche, INRIA
M. Valery Romanovski, Senior Researcher, University of Maribor
M. Mohab Safey El Din, Maître de Conférences, UPMC
M. Dongming Wang, Directeur de Recherche, CNRS

Departure date : 08/31/2011

2008-2012 Publications

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