Seminario Análisis y EDPs

Grassmannian reduction of Cucker-Smale systems and dynamical opinion games

Ponente:  Daniel Lear (University of Illinois at Chicago)
Fecha:  miércoles 30 de junio de 2021 - 15:00
Lugar:  Online - Info:

In this talk, we study a new class of alignment models with self-propulsion and Rayleigh-type friction forces, which describes the collective behavior of agents with individual characteristic parameters. We describe the long-time dynamics via a new method which allows to reduce analysis from the multidimensional system to a simpler family of two-dimensional systems parametrized by a proper Grassmannian. With this method we demonstrate exponential alignment for a large (and sharp) class of initial velocity configurations confined to a sector of opening less than $pi$. In the case when characteristic parameters remain frozen, the system governs dynamics of opinions for a set of players with constant convictions. Viewed as a dynamical non-cooperative game, the system is shown to possess a unique stable Nash equilibrium, which represents a settlement of opinions most agreeable to all agents. Such an agreement is furthermore shown to be a global attractor for any set of initial opinions. Joint work with David N. Reynolds & Roman Shvydkoy