I’m currently a permanent researcher at the French National Institute for Agricultural Research (INRA), in Montpellier (France). As a member of the MODEMIC INRA/INRIA project-team ( Modelling and optimisation of the dynamics of ecosystems with micro-organisms), I develop some methods for the study of microbial ecosystems.
Micro-organisms are present in numerous systems with agricultural or environmental interest. Some of them can be useful, as it is the case of the bacteria used in waste water treatment to degrade some undesirable substrates, or the yeasts responsible for the transformation of sugar into ethanol (wine fermentation). Other ones can be dangerous, as the cyanobacteria of some lakes can produce strong cyanotoxins.
My research project focuses on the study and the use of some classes of dynamical models for the microbial ecosystems. This project is composed of three main axes: one methodological axis, one thematic axis and one applicative axis.
- Axis 1: Resolution of dynamical problems for some classes of integro-differential population models. I study integro-differential population equations, with a special interest on the distributed delay equations, which are a particular case of time integro-differential equations. This kind of equations is often used for the modeling of microbial ecosystems. As for example, the Volterra integral equations have been proposed for the modeling of dynamic population. To study the distributed delay systems, I use the theory of diffusive representation, which I have studied during my Ph.D. thesis. My goal is to develop some methods for the simulation, the identification and the control of or by means of integro-differential models.
- Axis 2: Study of microbial ecosystems by use of infinite dimensional models. Models of microbial ecosystems of ODE type (Ordinary Differential Equations) have been widely studied, because of their relative “simplicity”. They enabled to better understand the functioning of the ecosystems. However, some heterogeneities (of the environment, the substrate, or even the microbial community itself) are most of the time neglected or greatly simplified in these models. Yet these heterogeneities could be at the origin of the biodiversity which is observed in the nature. To represent these heterogeneities, partial differential equations (PDE) can be used. My objective is to propose some models of ecosystems which take these heterogeneities into account, and to use them to study the impact of these heterogeneities on the functioning of the ecosystems.
- Axis 3 : control of bioprocesses. Some micro-organisms are used in bio-processes because of their skills (degradation of some substrate, transformation of some components, etc). To control such processes, we need to develop some specific methods, the classical methods of the control theory being mostly devoted to physical systems. Indeed, the biological systems have some particularities which have to be taken into account in the control design. First, the models are ill-known (and therefore less reliable), of great dimension (or even of infinite dimension) and strongly nonlinear. Moreover, only a few measurements are generally available online. My objective is therefore to develop some specific methods for the control of bioprocesses involving micro-organisms (micro-algae, yeasts, etc).