Consensus and flocking:
self-organized dynamics from particle to hydrodynamic descriptions
Tadmor, University of Maryland
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 and traffic flows to the formation of flocks of birds or
school of fish, tumor growth etc.
We introduce a new particle-based model, driven by self-alignment,
which addresses several drawbacks of existing models for
self-organized dynamics. The model is independent of the
number of agents: only their geometry in phase space is
involved. We will explain the emerging consensus and
unconditional flocking behavior in the proposed model in the
presence of non-symmetric interactions which decay
sufficiently slow, and discuss the difficulties with tracing
graph connectivity otherwise. The methodology carries over
from particle to kinetic and hydrodynamic descriptions.