Rigorous approaches to mathematical models of synchronization.
Publications and Preprints.
On oscillator death in the Winfree model
Forthcoming manuscript.
Vertical versus horizontal Poincaré inequalities on simply connected nilpotent Lie groups and groups of polynomial growth Submitted.
arXiv Preprint
Asymptotic formation and orbital stability of phase-locked states in Kuramoto–Lohe type synchronization models on Lie groups Submitted.
arXiv Preprint
Embedding snowflakes of Carnot groups into bounded dimensional Euclidean spaces with optimal distortion
Analysis & PDE. 15-8, 1933-1990 (2022) arXiv
Constants of motion for the Lohe model with frustration and its applications to emergent dynamics
(with Seung-Yeal Ha, Dohyun Kim, Hansol Park). Physica D: Nonlinear Phenomena. 416, 132781 (2021) arXiv
Asymptotic phase-locking dynamics and critical coupling strength for the Kuramoto model
(with Seung-Yeal Ha). Commun. Math. Phys. 377, 811-857 (2020) arXiv
On the relaxation dynamics of Lohe oscillators on some Riemannian manifolds
(with Seung-Yeal Ha, Dongnam Ko). J. Stat. Phys. 172, 1427-1478 (2018)
Emergence of partial locking states from the ensemble of Winfree oscillators
(with Seung-Yeal Ha, Dongnam Ko, Jinyeong Park). Quart. Appl. Math. 75, 39-68 (2017)
Emergent dynamics of a generalized Lohe model on some class of Lie groups
(with Seung-Yeal Ha, Dongnam Ko). J. Stat. Phys.
168, 171-207 (2017)
On the finiteness of collisions and phase-locked states for the Kuramoto model
(with Seung-Yeal Ha, Hwa Kil Kim). J. Stat. Phys.
163, 1394-1424 (2016)
Emergence of phase-locked states for the Kuramoto model in a large coupling regime
(with Seung-Yeal Ha, Hwa Kil Kim). Commun.
Math. Sci. 14, 1073-1091 (2016)
On the emergence and orbital stability of phase-locked states for the Lohe model
(with Seung-Yeal Ha). J. Stat. Phys. 163,
411-439 (2016)
Emergent dynamics of Winfree oscillators on locally coupled networks
(with Seung-Yeal Ha, Dongnam Ko, Jinyeong Park). J. Differential Equations 260, 4203-4236 (2016)
Emergence of phase-locked states for the Winfree model in a large coupling regime
(with Seung-Yeal Ha, Jinyeong Park), Discrete and Continuous Dynamical Systems 35, 3417-3436 (2015)
NB. Publications 1-10 were published under my previous name "Sang Woo Ryoo".
