On the Cucker-Smale ensemble with q-closest neighbors under time-delayed communications
- Authors
- Dong, Jiu-Gang; Ha, Seung-Yeal; Kim, Doheon
- Issue Date
- Aug-2020
- Publisher
- American Institute of Mathematical Sciences
- Keywords
- Collective dynamics; Cucker-Smale model; Monocluster flocking; Multi-agent system; Nonlinear functional
- Citation
- Kinetic and Related Models, v.13, no.4, pp 653 - 676
- Pages
- 24
- Indexed
- SCIE
SCOPUS
- Journal Title
- Kinetic and Related Models
- Volume
- 13
- Number
- 4
- Start Page
- 653
- End Page
- 676
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/114174
- DOI
- 10.3934/krm.2020022
- ISSN
- 1937-5093
1937-5077
- Abstract
- We study time-asymptotic interplay between time-delayed communication and Cucker-Smale (C-S) velocity alignment. For this, we present two sufficient frameworks for the asymptotic ocking to the continuous and discrete C-S models with q-closest neighbors in the presence of time-delayed communications. Communication time-delays result from the finite-propagation speed of information and they are often ignored in the first place modeling of collective dynamics. In the absence of time-delays in communication, Cucker and Dong showed that the C-S model with q-closest neighbors can exhibit a phase-transition like phenomenon for unconditional and conditional ockings depending on the size q relative to system size. In this paper, we investigate whether Cucker and Dong's result is robust with respect to the time-delayed communications or not. In fact, our ocking estimates show that the critical number of q for unconditional ocking is the same as in the case for zero timedelay, which shows the robustness of the Cucker and Dong's result with respect to small time-delay. © American Institute of Mathematical Sciences.
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