Non-flocking and flocking for the Cucker-Smale model with distributed time delays |
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| Institution: | 1. Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi 330031, PR China;2. Faculty of Engineering and Environment, University of Northumbria at Newcastle, Newcastle upon Tyne, NE1 8ST, UK;1. Department of Mathematics, College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, 410073, PR China;2. Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB E3B 5A3, Canada;3. Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3 Canada;1. National Institute for Mathematical Sciences, 70, Yuseong-daero 1689 beon-gil, Yuseong-gu, Daejeon, 34047, Republic of Korea;2. Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of Korea |
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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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