Multiflocks: Emergent Dynamics in Systems with Multiscale Collective Behavior
Roman Shvydkoy, Eitan Tadmor · Multiscale Modeling and Simulation · 2021
We study the multiscale description of large-time collective behavior of agents driven by alignment. The resulting multiflock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in turn peak at different time scales. We derive a “master-equation” which describes a complex multiflock congregations governed by two ingredients: (i) a fast inner-flock communication; and (ii) a slow(-er) interflock communication. The latter is driven by macroscopic observables which feature the up-scaling of the problem. We extend the current monoflock theory, proving a series of results which describe rates of multiflocking with natural dependencies on communication strengths. Both agent-based, kinetic, and hydrodynamic descriptions are considered, with particular emphasis placed on the discrete and macroscopic descriptions.