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FLOCKING AND COLLISION AVOIDANCE OF A CUCKER-SMALE TYPE SYSTEM WITH SINGULAR WEIGHTS
Maoli Chen,Xiang Li,Xiao Wang,Yicheng Liu
Keywords:Time-asymptotic ?ocking, Singular weights, Collision avoidance
Abstract:
      Due to the process of ?ocking behavior evolution, collision are automatic and should be considered in the ?ocking modeling. To overcome the collision between agents in the ?ock models, we combine a singular communication rate and extra interaction terms into Cucker-Smale model and study its ?ocking dynamics and o?er a rigorous analysis of collision-free mechanism. When the agents do not collide at the initial time, the su?cient condition of ?ock model is established. We further show that as the passage of time, a compact equilibrium con?guration may emergent.