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

@article{Haskovec2021ASP, 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.}, year={2021}, volume={20}, pages={130-148} }

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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