Title: Mathematical aspects of collective dynamics: consensus, the emergence of leaders and social hydrodynamics


Speaker: Eitan Tadmor
(University of Maryland)

Date: August 11
Time: 19:00 - 20:00
Room: Ballroom C

Chair: L. Pamela Cook


Abstract: We discuss the dynamics of systems driven by the “social engagement” of agents with their neighbors. Prototype models for such environmental averaging originate with opinion dynamics in human networks, flocking, self-organization of biological organisms, and rendezvous of mobile systems.

Two natural questions arise in this context -- what is the large time behavior of such systems, and what is the effective dynamics when the number of their agents tends to infinity. The underlying issue as time tends to infinity is how different rules of engagement influence the formation of clusters and in particular, the emergence of “consensus.” We propose an alternative paradigm based on the tendency of agents “to move ahead” which leads to the formation of trails and emergence of leaders. Different descriptions of collective dynamics arise when the number of agents tends to infinity, with the formation of Dirac masses at the kinetic level of description, and critical thresholds at the level of social hydrodynamics.

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