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Chiffres janvier 2014
Leçons Jacques-Louis Lions 2016 11h30 : mini-cours 3 : E. Tadmor
15 juin 2016 : 11h30—13h00
Eitan Tadmor (Université du Maryland)
Collective dynamics: flocking, emergence of patterns and social hydrodynamics
(3ème séance du mini-cours des Leçons Jacques-Louis Lions 2016)
This mini-course is focused on the dynamics of systems driven by the “social engagement” of agents with their neighbors. Prototype models based on environmental averaging are found in opinion and crowd dynamics of human networks, flocking, self-organization of biological organisms, and rendezvous of mobile systems.
We begin with a survey of several classical models of agent-based systems. We then follow with two natural questions that arise in the context of such systems: what is their large time behavior and what is the effective dynamics when the number of their agents tends to infinity.
The underlying issue of the first question is the emergence over time of large-scale patterns, and in particular, how different rules of engagement influence the formation of clusters e.g., 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.
The second question is concerned with different descriptions of collective dynamics which arise with large crowds of agents, and in particular, the formation of Dirac masses at the kinetic level of description, and the study of critical thresholds for macroscopic regularity at the level of social hydrodynamics.