Transient behavior of biological loop models with application to the Droop model

In this paper we study the transient behavior of a class of nonlinear differential systems verifying sign conditions through the succession of extrema of the state variables. This analysis does not depend, for the main part, on the analytical formulation of the model. The possible scenarios of sequences for the extrema, are represented on a graph and can be compared with the experimental data to validate the model. An application to the Droop model illustrates this method; we obtain as a result the global stability of the equilibrium and the possible successions of the extrema.