# Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime

@article{Haskovec2020AsymptoticFI, title={Asymptotic flocking in the Cucker-Smale model with reaction-type delays in the non-oscillatory regime}, author={Jan Haskovec and Ioannis Markou}, journal={Kinetic \& Related Models}, year={2020} }

We study a variant of the Cucker-Smale system with reaction-type delay. Using novel backward-forward and stability estimates on appropriate quantities we derive sufficient conditions for asymptotic flocking of the solutions. These conditions, although not explicit, relate the velocity fluctuation of the initial datum and the length of the delay. If satisfied, they guarantee monotone decay (i.e., non-oscillatory regime) of the velocity fluctuations towards zero for large times. For the…

## 16 Citations

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