Romain Ducasse: Influence of lines with fast diffusion on an ecological niche

mardi 7 janv. 2020, 14:45 → 15:30 Europe/Paris

Fokko du Cloux (Bâtiment Braconnier)

We present a model describing the influence of a line with fast diffusion - such as a road, or any kind of fast transportation network - on an ecological niche.

This model consists in a system of reaction-diffusion equations, set on domains with different dimensions.

We will first introduce some tools necessary to the study of such systems. In particular, we present a notion of ``generalized principal eigenvalue".

We will then study some qualitative properties (``extinction", ``persistence"...) of our system. First, we will see that the effect of a line with fast diffusion is always deleterious, and can even induce enough instability to drive a population to extinction. Then, we consider the case where the environment can move (as a result of a climate change, for instance). In this case, the presence of the line with fast diffusion can help the population to survive.