Approximation of dynamical systems using S-systems theory : application to biological systems
<|reference_start|>Approximation of dynamical systems using S-systems theory : application to biological systems: 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.<|reference_end|>
@article{tournier2005approximation,
    title={Approximation of dynamical systems using S-systems theory : application
  to biological systems},
    author={Laurent Tournier (LMC - IMAG)},
    journal={arXiv preprint arXiv:cs/0503008},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0503008},
    primaryClass={cs.SC math.DS q-bio.MN}
}