Branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic plan) that transports a given source onto a given target measure along a 1-dimensional network, the transportation cost per unit length is supposed in these models to be proportional to a concave power $\alpha \in (0,1)$ of the intensity of the flow.
The talk focuses on the stability for optimal traffic plan, with respect to variations of the source and target measures. The stability of optimal traffic plans was known when $\alpha$ is bigger than a critical threshold, but can be generalized to all exponents with no restriction on the class of measures.
