29 citations · 142 across the 32 of their papers we have counts for
6 papers · 1 filter
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…