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On the emergence of local flocking phenomena in Cucker-Smale ensemble
쿠커-스메일 집단에서의 국소적 플로킹 현상 창발에 관하여

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Authors
고동남
Advisor
하승열
Major
자연과학대학 수리과학부
Issue Date
2018-02
Publisher
서울대학교 대학원
Keywords
Cucker-Smale modelcritical coupling strengthhydrodynamic modelflockingmulti-cluster flockingdynamical system
Description
학위논문 (박사)-- 서울대학교 대학원 : 자연과학대학 수리과학부, 2018. 2. 하승열.
Abstract
We study the Cucker-Smale model which describes the flocking phenomena. In detail, we focus on the sufficient conditions to achieve the local flocking phenomena in various scenarios and models. The Lyapunov functional approach and bootstrapping argument play key roles to prove the asymptotic stability on emergence of flocking along time evolution. In the Cucker-Smale model, the dynamics of the particles are presented by the couplings proportional to the relative velocities between each pair of particles. The sufficient condition to the global flocking was suggested by Cucker and Smale, while necessary condition or local flocking was not analytically studied.
Our interests covers not only the Cucker-Smale particle model, but also the unit-speed model and the hydrodynamic model. The unit-speed model breaks the symmetry of equations and the hydrodynamic model needs the existence of solutions. The hydrodynamic equations are the macroscopic description through the mean-field limit process of the particle model. We avoid free boundary problems by describing Lagrangian variables.
Language
English
URI
https://hdl.handle.net/10371/141146
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Theses (Ph.D. / Sc.D._수리과학부)
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