A Simple Proof of Asymptotic Consensus in the Hegselmann-Krause and Cucker-Smale Models with Normalization and Delay

  title={A Simple Proof of Asymptotic Consensus in the Hegselmann-Krause and Cucker-Smale Models with Normalization and Delay},
  author={Jan Haskovec},
  journal={SIAM J. Appl. Dyn. Syst.},
  • J. Haskovec
  • Published 27 May 2020
  • Mathematics
  • SIAM J. Appl. Dyn. Syst.
We present a simple proof of asymptotic consensus in the discrete Hegselmann-Krause model and flocking in the discrete Cucker-Smale model with renormalization and variable delay. It is based on convexity of the renormalized communication weights and a Gronwall-Halanay-type inequality. The main advantage of our method, compared to previous approaches to the delay Hegselmann-Krause model, is that it does not require any restriction on the maximal time delay, or the initial data, or decay rate of… 
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