Papers
Fast and slow velocity alignments in a Cucker-Smale ensemble with adaptive couplings
- Research Fields의료수학연구부
- AuthorSeung-Yeal Ha; Dohyun Kim, Jinyeong Park
- JournalCommunications on Pure and Applied Analysis 19(9) (2020
- Link https://doi.org/10.3934/cpaa.2020209
- Classification of papersSCIE
- KeywordAdaptive coupling, collective behavior, Cucker-Smale model, emergence, flocking, Hebbian learning.
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.
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.