English

Multi-flocks: emergent dynamics in systems with multi-scale collective behavior

Analysis of PDEs 2020-03-11 v1 Adaptation and Self-Organizing Systems

Abstract

We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock 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 multi-flock congregations governed by two ingredients: (i) a fast inner-flock communication; and (ii) a slow(-er) inter-flock communication. The latter is driven by macroscopic observables which feature the up-scaling of the problem. We extend the current mono-flock theory, proving a series of results which describe rates of multi-flocking 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.

Keywords

Cite

@article{arxiv.2003.04489,
  title  = {Multi-flocks: emergent dynamics in systems with multi-scale collective behavior},
  author = {Roman Shvydkoy and Eitan Tadmor},
  journal= {arXiv preprint arXiv:2003.04489},
  year   = {2020}
}