This paper presents a review and critical analysis on the modeling of the dynamics of
vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It …

Synchronization of weakly coupled oscillators is ubiquitous in biological and chemical
complex systems. Recently, research on collective dynamics of many-body systems has …

We study the Kuramoto model for coupled oscillators. For the case of identical natural
frequencies, we give a new proof of the complete frequency synchronization for all initial …

We study the emergence of phase-locked states to the finite-dimensional Kuramoto model
from generic initial configurations which are not phase-locked states in a large coupling …

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 …

Synchronization as a typical collective phenomenon emerges in many complex systems,
and has attracted world-wide attention from science, engineering, sociology, and so forth …

In this paper, we present an asymptotic formation of phase-locked states from the ensemble
of Kuramoto oscillators with a symmetric and connected interaction topology. For a limited …

We study the synchronization of Kuramoto oscillators with adaptive coupling in interacting
networks. Network dynamics preserves the sum of all incoming pairwise coupling strengths …

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 study the asymptotic clustering (phase-locking) dynamics for the Kuramoto model. For
the analysis of emergent asymptotic patterns in the Kuramoto flow, we introduce the …