Related papers: Quantum Effects on the Synchronization Dynamics of…
Globally coupled ensembles of phase oscillators serve as useful tools for modeling synchronization and collective behavior in a variety of applications. As interest in the effects of simplicial interactions (i.e., non-additive, higher-order…
This paper studies a mean field game formulation of the classical Kuramoto model for synchronization. Our model captures the diversity within the population by considering random intrinsic frequencies, which allows us to study the impact of…
The synchronization transition of correlated ensembles of coupled Kuramoto oscillators on sparse random networks is investigated. Extensive numerical simulations show that correlations between the native frequencies of adjacent oscillators…
We have compared the phase synchronization transition of the second order Kuramoto model on 2D lattices and on large, synthetic power grid networks, generated from real data. The latter are weighted, hierarchical modular networks. Due to…
We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between…
We investigate the synchronization transition of the Shinomoto-Kuramoto model on networks of the fruit-fly and two large human connectomes. This model contains a force term, thus is capable of describing critical behavior in the presence of…
Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It…
We describe how the transition to synchronization in a system of globally coupled Stuart-Landau oscillators changes from continuous to discontinuous when the nature of the coupling is moved from diffusive to reactive. We explain this…
We investigate the magnetic quantum phase-transitions in bulk correlated metals at the level of dynamical mean-field theory. To this end, we focus on the Hubbard model on a simple cubic lattice as a function of temperature and electronic…
In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control…
We explore the collective phase dynamics of Wien-bridge oscillators coupled resistively. We carefully analyze the behavior of two coupled oscillators, obtaining a transformation from voltage to effective phase. From the phase dynamics we…
Common models of synchronizable oscillatory systems consist of a collection of coupled oscillators governed by a collection of differential equations. The ubiquitous Kuramoto models rely on an {\em a priori} fixed connectivity pattern…
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 this system, and show that for certain connection topologies…
The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by…
In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
The mean-field Kuramoto model for synchronization of phase oscillators with an asymmetric bimodal frequency distribution is analyzed. Breaking the reflection symmetry facilitates oscillator synchronization to rotating wave phases. Numerical…
Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…
We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the…
The Kuramoto model is the simplest case of globally coupled phase oscillators with a purely sinusoidal fundamental-harmonic phase coupling function, whose dynamical properties have been extensively studied. While coupled phase oscillators…