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Asymptotic ?ocking velocity and position formulas for the delayed Cucker-Smale model
Fen Nie,Yicheng Liu
Keywords:Cucker-Smale model; ?ocking solution; delay adaptation; ?ocking velocity formula; ?xed point.
Abstract:
      The Cucker-Smale (short for C-S) model was modified by introduced multiple time delays, and the flocking characteristics of the processing delay C-S model of systems was obtained. based on the fixed point theorem, we present the existence and uniqueness of the flocking solution for our delayed C-S model when the influence function has the property of Lipschitz and the initial value satisfies certain conditions. At last, we present the asymptotic flocking velocity and the final relative position between agents of the unique flocking solution for such system.