In this chapter, we present the Cucker–Smale-type flocking models and discuss their
mathematical structures and flocking theorems in terms of coupling strength, interaction
topologies, and initial data. In 2007, two mathematicians Felipe Cucker and Steve Smale
introduced a second-order particle model which resembles Newton's equations in N-body
system and present how their simple model can exhibit emergent flocking behavior under
sufficient conditions expressed only in terms of parameters and initial data. After Cucker …

In this chapter, we present the Cucker-Smale type flocking models, and discuss their
mathematical structures and flocking theorems in terms of coupling strength, interaction
topologies and initial data. In 2007, two mathematicians Felipe Cucker and Steve Smale
introduced a second-order particle model which resembles Newton's equations in $ N $-
body system, and present how their simple model can exhibit emergent flocking behavior
under sufficient conditions expressed only in terms of parameters and initial data. After …