Kinetic Description of Social Dynamics: From Consensus to Flocking

Consensus and flocking and heterophilious self-alignment in agent-based models

Eitan Tadmor

University of Maryland

Self-organized dynamics is driven by the interaction of agents with their neighbors. Examples range from consensus of voters and traffic flows to the formation of flocks of birds and tumor growth. When the interaction consists of global self-alignment, the large time behavior leads into consensus or flocking. When the self-alignment is local, the dynamics evolves into one or more clusters and the open questions regarding the emergence of consensus are related to the connectivity of the underlying graph, depending on the heterophilious character of the dynamics. At the hydrodynamic level, the large time behavior is dictated by the balance between nonlinear convection and convolution-based interaction based on non-local means. Finite time breakdown depends on whether the initial configuration crosses intrinsic, O(1) critical thresholds (CT). We demonstrate this CT phenomena with several n-dimensional prototype models. These include prolonged life-span of sub-critical 2D shallow-water solutions, 3D restricted Euler and Euler-Poisson equations, and the hydrodynamic descriptions of self-organized dynamics.