We consider the wellknown LiebLiniger (LL) model for
In this note we study a new class of alignment models with selfpropulsion and Rayleightype 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 us to reduce analysis from the multidimensional system to a simpler family of twodimensional 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
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 noncooperative 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.
 Award ID(s):
 1813351
 Publication Date:
 NSFPAR ID:
 10329374
 Journal Name:
 Discrete & Continuous Dynamical Systems
 Volume:
 41
 Issue:
 12
 Page Range or eLocationID:
 5765
 ISSN:
 10780947
 Sponsoring Org:
 National Science Foundation
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