Collective dynamics: emergence of consensus and social hydrodynamics

Prototypical models for collective dynamics are found in opinion dynamics, flocking, self-organization of biological organisms, and rendezvous in mobile networks. They are driven by the “social engagement” of agents with their local neighbors.

We discuss the emergent behavior of such systems. Their large-time behavior leads to the emergence of different patterns, depending on the propagation of connectivity of the underlying graphs. In particular, global interactions lead to the emergence of consensus, leaders etc. The collective dynamics of large crowds of agents lend itself to “social hydrodynamics”, driven by the corresponding engagement through local means. We discuss the global regularity of social hydrodynamics for sub-critical initial configurations.