Qualitative dynamics of a class of nonlinear biological systems

In this paper we propose a methodology to analyze the global qualitative dynamics of a nonlinear class of differential systems which encompass numerous biological models. We show that, independently of parameters values, the possible succession with respect to time of some qualitative events characterizing transients of state variables (extrema, position ...) are strongly related to the signs of the Jacobian matrix. The method is illustrated with a set of models usually used to describe phytoplanctonic growth in a bioreactor. The corresponding transition graph is derived and compared with experimental data. This methodology applies well when some parameters are unknown, which is often the case in biological models. Copyright (C) 1998 IFAC.