22 citations · 47 across the 18 of their papers we have counts for
12 papers · 1 filter
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…
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…
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…
Constants of motion for the finite-dimensional Lohe type models with frustration and applications to emergent dynamics
Seung-Yeal Ha, Dohyun Kim, Hansol Park +1
We present constants of motion for the finite-dimensional Lohe type aggregation models with frustration and we apply them to analyze the emergence of collective behaviors. The Lohe…