Non-flocking and flocking for the Cucker-Smale model with distributed time delays

Zhang, Ziwei, Yin, Xiuxia and Gao, Zhiwei (2022) Non-flocking and flocking for the Cucker-Smale model with distributed time delays. Journal of the Franklin Institute. ISSN 0016-0032 (In Press)

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Abstract

In this paper, we study a flocking behavior that may or not appear for Cucker - Smale model with distributed time delays. For the short range communicated Cucker - Smale model, the flocking condition has strong restrictions on initial data. For this case, we mainly consider the non - flocking behavior. By establishing and appropriately estimating an inequality of the position variance such that the second order space moment is unbounded, we drive a sufficient condition for the non - existence of the asymptotic flocking when the time delays satisfy a suitable smallness assumption. Furthermore, we also provide a sufficient condition of asymptotic flocking. Finally, we present numerical simulations to validate the theoretical results.

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