Emergent dynamics of the Cucker-Smale flocking model and its variants

摘要

In this chapter, we present the Cucker-Smale type flocking models, anddiscuss their mathematical structures and flocking theorems in terms ofcoupling strength, interaction topologies and initial data. In 2007, twomathematicians Felipe Cucker and Steve Smale introduced a second-order particlemodel which resembles Newton's equations in $N$-body system, and present howtheir simple model can exhibit emergent flocking behavior under sufficientconditions expressed only in terms of parameters and initial data. AfterCucker-Smale's seminal works, their model has received lots of attention fromapplied math and control engineering communities. We discuss the state-of-artfor the flocking theorems to Cucker-Smale type flocking models.