We study the collective relaxation dynamics appearing in weakly coupled Lohe oscillators in
a large coupling regime. The Lohe models on the unit sphere and unitary group were …

The Kuramoto model of coupled phase oscillators is often used to describe synchronization
phenomena in nature. Some applications, eg, quantum synchronization and rigid-body …

We present and analyze a nonabelian version of the Kuramoto system, which we call the
Quantum Kuramoto system. We study the stability of several classes of special solutions to …

The dynamic behavior of Lohe oscillators on the unit sphere is examined under attractive
and repulsive couplings. We introduce an order parameter measuring the degree of …

In this article, we present a new Cucker-Smale model on smooth Riemannian manifolds
using the concepts of covariant derivative and parallel transport, and we also study its …

We partially integrate a system of rectangular matrix Riccati equations which describe the
synchronization behavior of a nonlinear complex system of N globally connected oscillators …

We introduce a Lohe group which is a new class of matrix Lie groups and present a
continuous dynamical system for the synchronization of group elements in a Lohe group …

Equilibria and consensus dynamics of the Lohe model with identical oscillators are
investigated under more general interconnection topologies. In the existing literatures on the …

We present an improved exponential frequency synchronization estimate for globally
coupled Kuramoto oscillators. For a sufficiently large coupling, it is numerically observed that …

We present a new aggregation model on the space of rank-m tensors with the same size,
and study emergent dynamics of the proposed model. Our proposed new aggregation …