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FAST AND SLOW VELOCITY ALIGNMENTS IN A CUCKER-SMALE ENSEMBLE WITH ADAPTIVE COUPLINGS
- Authors
- Ha, Seung-Yeal; Kim, Dohyun; Park, Jinyeong
- Issue Date
- Sep-2020
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- Adaptive coupling; collective behavior; Cucker-Smale model; emergence; flocking; Hebbian learning
- Citation
- COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, v.19, no.9, pp.4621 - 4654
- Indexed
- SCIE
SCOPUS
- Journal Title
- COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
- Volume
- 19
- Number
- 9
- Start Page
- 4621
- End Page
- 4654
- ISSN
- 1534-0392
- Abstract
- We study the emergent dynamics of the Cucker-Smale (C-S for brevity) ensemble under adaptive couplings. For the adaptive couplings, we basically consider two types of couplings: Hebbian vs. anti-Hebbian. When the Hebbian rule is employed, we present sufficient conditions leading to the mono-cluster flocking using the Lyapunov functional approach. On the other hand, for the anti-Hebbian rule, the possibility of mono-cluster flocking mainly depends on the integrability of the communication weight function and the regularity of the adaptive law at the origin. In addition, we perform numerical experiments and compare them with our analytic results.
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Related Researcher
- Park, Jin yeong
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)