Colloquium

Self-organized dynamics is driven by "rules of engagement", which describe how each agent interacts with its neighbors. They consist of long-term attraction, mid-range alignment and short-range repulsion. Many self-propelled models are driven by the balance between these three forces, which yield emerging structures of interest. Examples range from consensus of voters to flocking of birds.

We discuss particle-based models for self-organized dynamics, with a focus on a prototype model driven by non-symmetric self-alignment. We explain the emergence of consensus and unconditional flocking when the interactions decay is sufficiently slow. When the self-alignment is compactly supported, then there are open questions regarding clustering and the emerging consensus in heterophily dynamics. These questions are linked to the connectivity of the underlying graph. The methodology carries over from particle to kinetic and hydrodynamic descriptions.