Global Qualitative Behavior of a Class of Nonlinear Biological Systems; Application to the Qualitative Validation of Phytoplankton Growth Models

Olivier Bernard 1 Jean-Luc Gouzé
1 COMORE - Modeling and control of renewable resources
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this paper we propose a methodology to analyze the global qualitative behavior of a class of nonlinear differential systems with respect to their structure. This class of loop structured systems with monotonous interactions encompasses numerous biological models. We show that, independently of the parameters values or of the analytical formulation of the system, the possible successions with respect to time of some qualitative events that characterize the transients of state variables are strongly related to the signs of the Jacobian matrix (structure of the model). We propose a procedure to derive the transition graph; this graph summarizes the set of possible qualitative features for the state according to the structure of the model. The comparison of the graph with experimental (even noisy) data allows to validate directly this structure. The method is illustrated with a set of models usually used to describe phytoplanctonic growth in the chemostat. The corresponding transition graphis derived and compared with experimental data.
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RR-3334, INRIA. 1998
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Olivier Bernard, Jean-Luc Gouzé. Global Qualitative Behavior of a Class of Nonlinear Biological Systems; Application to the Qualitative Validation of Phytoplankton Growth Models. RR-3334, INRIA. 1998. 〈inria-00073355〉

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