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

In this article we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm uses 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 performed to converge towards an equilibrium, giving at the same time a S-system approximating the initial system around this equilibrium. This algorithm has been applied to a real biological example in 14 dimensions which is a subsystem of a metabolic pathway in Arabidopsis Thaliana.