Approximation of dynamical systems using S-systems theory : application to biological systems

Laurent Tournier (1)

1 LMC - IMAG - Laboratoire de Modélisation et Calcul

In this paper we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm implies a symbolic manipulation of ODE in order to give a local approximation of differential equations with power-law dynamics (S-systems). A numerical calculus is then needed to converge towards an equilibrium, giving at the same time a S-system approximating the initial system around this equilibrium. This algorithm is applied to a real biological example in 14 dimensions which is a subsystem of a metabolic pathway in Arabidopsis Thaliana.

Mots clés: Power-law; S-systems; Dynamical systems; Biochemical pathways

Domaines: Calcul formel [cs.SC]; Systèmes dynamiques [math.DS]; Autre [q-bio.OT]

Laurent Tournier. Approximation of dynamical systems using S-systems theory : application to biological systems. 2005. ⟨hal-00004351⟩