Emergence of stochastic flocking for the discrete Cucker-Smale model with randomly switching topologies
- Title
- Emergence of stochastic flocking for the discrete Cucker-Smale model with randomly switching topologies
- Author
- 김도헌
- Keywords
- Cucker-Smale model; randomly switching topology; directed graphs; flocking
- Issue Date
- 2019-12
- Publisher
- INT PRESS BOSTON
- Citation
- COMMUNICATIONS IN MATHEMATICAL SCIENCES; 2021, 19 1, p205-p228, 24p.
- Abstract
- We study emergent dynamics of the discrete Cucker-Smale (in short, DCS)
model with randomly switching network topologies. For this, we provide a sufficient framework leading to the stochastic flocking with probability one. Our sufficient framework is
formulated in terms of an admissible set of network topologies realized by digraphs and
probability density function for random switching times. As examples for the law of switching times, we use the Poisson process and the geometric process and show that these two
processes satisfy the required conditions in a given framework so that we have a stochastic
flocking with probability one. As a corollary of our flocking analysis, we improve the earlier
result [15] on the continuous C-S model.
- Description
- The work of J.-G. Dong is supported by the Fundamental Research Funds for the Central Universities. The work of S.-Y. Ha is supported by the National Research Foundation of Korea (NRF-2017R1A2B2001864), the work of J. Jung is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP): NRF-2016K2A9A2A13003815, 2019R1A6A1A10073437, and the work of D. Kim is supported by a KIAS Individual Grant (MG073901) at Korea Institute for Advanced Study.
- URI
- https://arxiv.org/abs/1912.11949https://repository.hanyang.ac.kr/handle/20.500.11754/172288
- Appears in Collections:
- COLLEGE OF SCIENCE AND CONVERGENCE TECHNOLOGY[E](과학기술융합대학) > APPLIED MATHEMATICS(응용수학과) > Articles
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