EMERGENT BEHAVIORS IN GROUP RING FLOCKS

被引：0

作者：

Ha, Seung-Yeal ^{[1
,2
,3
]}

Park, Hansol ^{[1
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea

[3] Korea Inst Adv Study, Hoegiro 85, Seoul 02455, South Korea

来源：

QUARTERLY OF APPLIED MATHEMATICS | 2021年 / 79卷 / 04期

基金：

新加坡国家研究基金会;

关键词：

PHASE-LOCKED STATES; KURAMOTO MODEL; SYNCHRONIZATION; STABILITY; DYNAMICS; OSCILLATORS; POPULATIONS; CONSENSUS; SYSTEMS;

D O I：

10.1090/qam/1595

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a first-order aggregation model on a group ring and investigate its asymptotic dynamics. In a positive coupling strength regime, we show that the flow generated by the proposed model approaches to an equilibrium manifold asymptotically using a nonlinear functional and LaSalle invariance principle. Moreover, we also verify that equilibrium manifold's structure is strongly dependent on the structure of an underlying group structure.

引用

页码：617 / 640

页数：24

共 54 条

[1] The Kuramoto model:: A simple paradigm for synchronization phenomena
Acebrón, JA
Bonilla, LL
Vicente, CJP
Ritort, F
Spigler, R
[J]. REVIEWS OF MODERN PHYSICS, 2005, 77 (01) : 137 - 185
[2] Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives
Albi, G.
Bellomo, N.
Fermo, L.
Ha, S. -Y.
Kim, J.
Pareschi, L.
Poyato, D.
Soler, J.
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2019, 29 (10) : 1901 - 2005
[3] OPINION DYNAMICS ON A GENERAL COMPACT RIEMANNIAN MANIFOLD
Aydogdu, Aylin
McQuade, Sean T.
Duteil, Nastassia Pouradier
[J]. NETWORKS AND HETEROGENEOUS MEDIA, 2017, 12 (03) : 489 - 523
[4] ON THE COMPLETE PHASE SYNCHRONIZATION FOR THE KURAMOTO MODEL IN THE MEAN-FIELD LIMIT
Benedetto, Dario
Caglioti, Emanuele
Montemagno, Umberto
[J]. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2015, 13 (07) : 1775 - 1786
[5] A Matrix-Valued Kuramoto Model
Bronski, Jared C.
Carty, Thomas E.
Simpson, Sarah E.
[J]. JOURNAL OF STATISTICAL PHYSICS, 2020, 178 (02) : 595 - 624
[6] BIOLOGY OF SYNCHRONOUS FLASHING OF FIREFLIES
BUCK, J
BUCK, E
[J]. NATURE, 1966, 211 (5049) : 562 - &
[7] Emergent behaviors of a holonomic particle system on a sphere
Chi, Dongpyo
Choi, Sun-Ho
Ha, Seung-Yeal
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (05)
[8] Complete Entrainment of Lohe Oscillators under Attractive and Repulsive Couplings
Choi, Sun-Ho
Ha, Seung-Yeal
[J]. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2014, 13 (04): : 1417 - 1441
[9] Quantum synchronization of the Schrodinger-Lohe model
Choi, Sun-Ho
Ha, Seung-Yeal
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2014, 47 (35)
[10] Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model
Choi, Young-Pil
Ha, Seung-Yeal
Jung, Sungeun
Kim, Yongduck
[J]. PHYSICA D-NONLINEAR PHENOMENA, 2012, 241 (07) : 735 - 754

← 1 2 3 4 5 6 →