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We study a variant of the Cucker-Smale system with reaction-type delay. Usingnovel backward-forward and stability estimates on appropriate quantities wederive sufficient conditions for asymptotic flocking of the solutions. Theseconditions, although not explicit, relate the velocity fluctuation of theinitial datum and the length of the delay. If satisfied, they guaranteemonotone decay (i.e., non-oscillatory regime) of the velocity fluctuationstowards zero for large times. For the simplified setting with only two agentsand constant communication rate the Cucker-Smale system reduces to the delaynegative feedback equation. We demonstrate that in this case our methodprovides the sharp condition for the size of the delay such that the solutionbe non-oscillatory. Moreover, we comment on the mathematical issues appearingin the formal macroscopic description of the reaction-type delay system.

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