4 papers
Relaxation dynamics of the Inertial Winfree model
Caiman Moreno-Earle, Seung-Yeon Ryoo, Grace To
We prove two synchronization theorems for the second-order (inertial) Winfree model of coupled oscillators. The first result is a pathwise oscillator-death theorem with explicit sm…
Emergent behaviors of Winfree oscillators on special orthogonal group
Seung-Yeal Ha, Chaejoo Lee, Eunjun Lee +2
We propose a generalized matrix-valued synchronization model which can be regarded as matrix generalization of the classical Winfree model to the special orthogonal group, and we p…
Quantitative relaxation dynamics from generic initial configurations in the inertial Kuramoto model
Hangjun Cho, Jiu-Gang Dong, Seung-Yeal Ha +1
We study the relaxation dynamics of the inertial Kuramoto model toward a phase-locked state from a generic initial phase configuration. For this, we propose a sufficient framework…
Inertia perturbation theory for the inertial Kuramoto model
Hangjun Cho, Jiu-Gang Dong, Seung-Yeal Ha +1
In this work, we study the inertial Kuramoto model, which is a second-order extension of the classical first-order Kuramoto model, as an inertial perturbation of the first-order Ku…