Research topics

• Ordinary differential equations, Dynamical systems, 

• Averaging, 

• Singular Perturbations, 

• Biology and other natural sciences, 

• Convex and discrete geometry, 

• Difference and functional equations, 

• Differential geometry, 

• General topology, 

• Mathematical logic and foundations, Nonstandard analysis, 

• Information and communication,

• Operations research, Mathematical programming
  
  

Current research activity

I am interested about the mathematical theory of the chemostat and the understanding of the mechanisms of coexistence of competing species on a single substrate. The studied mechanisms are the density dependence of the growth functions, the  flocculation of bacteria, the inhibition and the syntrophic relationship. I develop these studies mainly with PhDs students of the Treasure network. I am also interested in the fragmentation of habitats and the SLOSS (Single Large or Several Small) debate and the dispersal inuced growth (DIG) phenomenon. 

I am working to offer simple but realistic models that are complex enough to capture the essential dynamic characteristics of the processes under study but, on the other hand, simple enough to make it possible to make an analytical study of them without specifying the parameters. These models for understanding are a useful complement to more complex models for action, which take into account reality in greater detail, such as the Anaerobic Digestion Model No.1 (ADM1), but which can only be approached through numerical simulations.