29 citations · 142 across the 32 of their papers we have counts for
11 papers · 1 filter
An algebraic approach for the weak coupling of multiple Lohe tensor models
Seung-Yeal Ha, Dohyun Kim, Hansol Park
We present a systematic algebraic approach for the weak coupling of Cauchy problems to multiple Lohe tensor models. For this, we identify an admissible Cauchy problem to the Lohe t…
Emergent behaviors of discrete Lohe aggregation flows
Hyungjun Choi, Seung-Yeal Ha, Hansol Park
The Lohe sphere model and the Lohe matrix model are prototype continuous aggregation models on the unit sphere and the unitary group, respectively. These models have been extensive…
Relaxation dynamics of SIR-flocks with random epidemic states
Seung-Yeal Ha, Hansol Park, Seoyeon Yang
We study the collective dynamics of a multi-particle system with three epidemic states as an internal state. For the collective modeling of active particle system, we adopt modelin…
A velocity alignment model on quotient spaces of the Euclidean space
Hansol Park
The Cucker-Smale(CS) model is a velocity alignment model, and this model also has been generalized on general manifolds. We modify the CS model on manifolds to get rid of a-priori…
Emergent behaviors of the kinetic Lohe Hermitian sphere model
Junhyeok Byeon, Seung-Yeal Ha, Gyuyoung Hwang +1
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 ten…
Existence and emergent dynamics of quadratically separable states to the Lohe tensor model
Seung-Yeal Ha, Dohyun Kim, Hansol Park
A tensor is a multi-dimensional array of complex numbers, and the Lohe tensor model is an aggregation model on the space of tensors with the same rank and size. It incorporates pre…
The Watanabe-Strogatz transform and constant of motion functionals for kinetic vector models
Hansol Park
We present a kinetic version of the Watanabe-Strogatz(WS) transform for vector models in this paper. From the generalized WS-transform, we obtain the cross-ratio type constant of m…
Emergent behaviors of rotation matrix flocks
Razvan C. Fetecau, Seung-Yeal Ha, Hansol Park
We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group by identifying closed form expressions for geometric quantities such as…
Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics
Hansol Park
We present a high-dimensional Winfree model in this paper. The Winfree model is the first mathematical model for synchronization on the circle. We generalize this model to the high…
Emergent behaviors of homogeneous Lohe Hermitian sphere particles under time-delayed interactions
Seung-Yeal Ha, Gyuyoung Hwang, Hansol Park
We study emergent behaviors of the Lohe hermitian sphere(LHS) model with a time-delay for a homogeneous ensemble. The LHS model is a complex counterpart of the Lohe sphere(LS) aggr…
Asymptotic interplay of states and adapted coupling gains in the Lohe hermitian sphere model
Junhyeok Byeon, Seung-Yeal Ha, Hansol Park
We study emergent dynamics of the Lohe hermitian sphere (LHS) model with the same free flows under the dynamic interplay between state evolution and adaptive couplings. The LHS mod…