Date : Mercredi 5 février 2025
Heure : 10h30
Salle : via Zoom, contacter la direction pour avoir le lien

Conférencière: Sana Jahedi, Postdoctoral Associate at the Department of Mathematics at the University of Maryland at College Park,

Titre : Structured Systems of Nonlinear Equations

Résumé : When modelling direct interactions within a community structure, we often end up with a system of ordinary differential equations that describes the population dynamics of species involved within the network. Often, we do not know the exact form of the interactions, whether it is linear or nonlinear. In the case of a nonlinear interaction, the nonlinearity type is often unknown.  Hence, it is hard to make inferences about the overall state of the complex system. A structured system of equations will help model such a scenario.

A structured system of equations, F(x)=c, is a system of M equations in which it is specified which of the N variables are allowed to appear in each equation, but the exact form of the function F is unknown.

Structured systems have an intensive application in the control theory. I will talk about the generic properties of structured systems. In the engineering literature, it is shown that almost every (in the sense of Lebesgue measure) matrix that respects a given structure has the same rank. I have extended this result to nonlinear structured systems using the concept of prevalence (the analogue of the Lebesgue measure for infinite dimensional vector space of functions). I will show that "almost every" (in the sense of prevalence) nonlinear function that respects a given structure has the same rank. A solution p of a system F(p)=c is called robust if it persists despite small changes in F. I will show that the robustness of solutions of structured systems is a generic property and when robustness fails in a structured system, it is due to the existence of a unique "minimax backward bottleneck", a feature of the directed graph of the system. I will characterize the unique "minimax bottleneck" and describe how the model structure could be redesigned to make it robust.

Voici les informations de la présentation de 30 minutes sur l’enseignement au 1er cycle :

Date : Mercredi 5 février 2025
Heure : 12h30
Salle : via Zoom, contacter la direction pour avoir le lien