Section: New Results

Distributed delay systems

Participant : Céline Casenave.

In microbial ecosystems, time delays are often present. For a long time (especially with V. Volterra), distributed delay models (or integro-differential equations) have been proposed to take into account these delays in population models. Some dynamic problems dealing with integro-differential models can be tackled in an original way by using the methodology called “diffusive representation”. Some works, which began during the PhD thesis of Céline Casenave, are still under development.

In [26] , a new formulation of an integro-differential model of a porous media is proposed, based on this methodology. From this formulation, the dissipative and passive features of the porous wall are established, and numerical simulations are performed. A reduced order model is also proposed which summarizes the boundary behavior of the porous wall ( (Two journal articles dealing with the identification of integro-differential models, and the controllability of some SISO Volterra models are still under revision.)).

This work is done in collaboration with LAAS (Univ. Toulouse III) and the Gipsa-lab (CNRS, Grenoble-INP, Univ. Joseph Fourier, Univ. Stendhal). In the future, these works could be adapted to the case of microbial ecosystems.