Controllability in Lotka-Volterra competitive systems with positive controls

Ecology models describing the evolution of population densities, as Lotka-Volterra competitive systems, require the solutions to be positive and bounded. Hence, the boundary controls have also to satisfy some constraints, so classic techniques in control theory cannot be applied. In this talk, we will describe non-controllability phenomena due to the presence of barrier solutions depending on the parameters of the systems. This is joint work with Enrique Zuazua.