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Last update: May 2021

Dynamical Systems Axe

MISTEA’s ‘Dynamical Systems’ axe brings together a scientific team (researchers, teacher-researchers, engineers, doctoral students, etc.) to carry out research in deterministic and stochastic mathematics for the analysis and control of agro-ecosystems.

The axe research works deals with the modelling, simulation, optimisation and control of dynamical systems representing the functioning of agro-ecosystems. These works are based on collaborations with research teams in agronomy, ecology and forestry.

The research themes of the axe are in two fields:

1) Modelling, simulation and analysis of systems.

The systems studied are either deterministic, most often based on systems of ordinary differential equations, or stochastic, most often Markovian. As far as deterministic models are concerned, both low-dimensional models allowing qualitative results to be obtained and more complex and realistic models are considered. With regard to stochastic methods, among the Markovian models, the Piecewise Deterministic Markov Models (PDMP) are more particularly studied. The methods developed concern the analysis of dynamic systems. In particular, the influence of hazards in the prediction of models and the identification of behaviour linked to climatic sequences in agronomy are studied. These analyses are based on sensitivity analysis of model responses to input variables and the propagation of uncertainties.

2) Optimisation and control.

The methods developed are of two kinds:

mathematical optimization of criteria based on physical, biological or economic aspects. Part of the work focuses on decision making in the presence of uncertainty and is based on dynamic programming. The applications are diverse and can concern the management of biotechnological processes as well as the management of renewable resources.
control of dynamical systems in process engineering or for environmental preservation. The fields of application of the methods developed in the axis have concerned depollution, forestry, lake ecosystems and alcoholic fermentation.

Permanent staff:

Céline Casenave (coordinator)
Bertrand Cloez
Bénédicte Fontez
Patrice Loisel
Alain Rapaport
Sébastien Roux