EMERGENT BEHAVIORS OF THE KINETIC LOHE HERMITIAN SPHERE MODEL

被引:0
作者
Byeon, Junhyeok [1 ]
Ha, Seung-yeal [2 ,3 ]
Hwang, Gyuyoung [2 ]
Park, Hansol [4 ]
机构
[1] Seoul Natl Univ, Res Inst Basic Sci, Seoul 08826, South Korea
[2] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea
[3] Seoul Natl Univ, Res Inst Math, Seoul 08826, South Korea
[4] Simon Fraser Univ, Dept Math, 8888 Univ Dr, Burnaby, BC V5A 1S6, Canada
关键词
Emergence; Kuramoto model; Lohe Hermitian sphere model; order parameter; PHASE-LOCKED STATES; KURAMOTO MODEL; SYNCHRONIZATION; STABILITY; DYNAMICS; OSCILLATORS; POPULATIONS;
D O I
暂无
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study a global well-posedness of measure-valued solutions to the kinetic Lohe Hermitian sphere (LHS) model derived from the Lohe tensor (LT) model on the set of rank-1 complex tensors (i.e. complex vectors) with the same size and investigate emergent behaviors. The kinetic LHS model corresponds to a complex analogue of the kinetic LS model which has been extensively studied in the literature on the aggregation modeling of Lohe particles on the unit sphere in Euclidean space. In this paper, we provide several frameworks in terms of system parameters and initial data leading to the local and global well-posedness of measure-valued solutions. In particular, we show emergent behaviors of the kinetic LHS model with the same free flows by analyzing the temporal evolution of the order parameter.
引用
收藏
页码:1171 / 1213
页数:43
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