29 citations · 142 across the 32 of their papers we have counts for
34 papers
Dimension-dependent symmetry breaking in a diffusive nonlocal interaction model
Dohyun Kim, Hansol Park, Woojoo Shim
We study the equilibrium structure and long-time behavior of a nonlinear Fokker--Planck equation with diffusion and nonlocal interactions generated by squared simplex volumes. For…
Finite-dimensional reduction of a Wasserstein gradient flow and sharp decay rates
Dohyun Kim, Hansol Park, Woojoo Shim
We study the Wasserstein gradient flow generated by a family of extended generalized variance functionals, defined as the expected squared -dimensional volume of a simplex, whic…
Aggregation-diffusion energies on Cartan-Hadamard manifolds of unbounded curvature
Razvan C. Fetecau, Hansol Park
We consider an aggregation-diffusion energy on Cartan-Hadamard manifolds with sectional curvatures that can grow unbounded at infinity. The energy corresponds to a macroscopic aggr…
Higher-order interaction model from geometric measurements
Dohyun Kim, Hansol Park, Woojoo Shim
We introduce a higher simplicial generalization of the linear consensus model which shares several common features. The well-known linear consensus model is a gradient flow with a…
Long-time behaviour of interaction models on Riemannian manifolds with bounded curvature
Razvan C. Fetecau, Hansol Park
We investigate the long-time behaviour of solutions to a nonlocal partial differential equation on smooth Riemannian manifolds of bounded sectional curvature. The equation models s…
Optimal consensus control models on the sphere
Hui Huang, Hansol Park
In this paper, we investigate the consensus models on the sphere with control signals, where both the first and second order systems are considered. We provide the existence of the…
Asymptotic convergence of heterogeneous first-order aggregation models: from the sphere to the unitary group
Dohyun Kim, Hansol Park
We provide the detailed asymptotic behavior for first-order aggregation models of heterogeneous oscillators. Due to the dissimilarity of natural frequencies, one could expect that…
Equilibria and energy minimizers for an interaction model on the hyperbolic space
Razvan C. Fetecau, Hansol Park
We study an intrinsic model for collective behaviour on the hyperbolic space $\bbh^\dm$. We investigate the equilibria of the aggregation equation (or equivalently, the critical po…
Mean field Kuramoto models on graphs
Wuchen Li, Hansol Park
One of a classical synchronization model is the Kuramoto model. We propose both first and second order Kuramoto dynamical models on graphs using discrete optimal transport dynamics…
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…
Emergent behaviors in group ring flocks
Seung-Yeal Ha, Hansol Park
We present a first-order aggregation model on a group ring, and study its asymptotic dynamics. In a positive coupling strength regime, we show that the flow generated by the propos…
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…
Collective behaviors of the Lohe hermitian sphere model with inertia
Seung-Yeal Ha, Myeongju Kang, Hansol Park
We present a second-order extension of the first-order Lohe hermitian sphere(LHS) model and study its emergent asymptotic dynamics. Our proposed model incorporates an inertial effe…
An intrinsic aggregation model on the special orthogonal group : well-posedness and collective behaviours
Razvan C. Fetecau, Seung-Yeal Ha, Hansol Park
We investigate an aggregation model with intrinsic interactions on the special orthogonal group . We consider a smooth interaction potential that depends on the squared intr…