相关论文: Linear stability of the incoherent solution and th…
We consider the mean-field noisy Kuramoto-Daido model, which is a McKean-Vlasov equation on the circle with bimodal interaction $W(\theta)=\cos\theta+m\cos2\theta$ for $m\ge 0$ and interaction strength $K$, generalizing the celebrated noisy…
Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…
We consider a recently introduced $D$-dimensional generalized Kuramoto model for many $(N\gg 1)$ interacting agents in which the agent states are $D$-dimensional unit vectors. It was previously shown that, for even $D$, similar to the…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
We present a linear stability analysis of the incoherent state in a system of globally coupled, identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and…
Recently, there has been considerable interest in the study of spontaneous synchronization, particularly within the framework of the Kuramoto model. The model comprises oscillators with distributed natural frequencies interacting through a…
We provide an analysis of the classic Kuramoto model of coupled nonlinear oscillators that goes beyond the existing results for all-to-all networks of identical oscillators. Our work is applicable to oscillator networks of arbitrary…
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling…
We study the synchronization of Kuramoto oscillators with all-to-all coupling in the presence of slow, noisy frequency adaptation. In this paper we develop a new model for oscillators which adapt both their phases and frequencies. It is…
The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as a coupled phase oscillators. In this paper, a bifurcation structure of the infinite dimensional Kuramoto model is…
We consider the (noisy) Kuramoto model, that is a population of N oscillators, or rotators, with mean-field interaction. Each oscillator has its own randomly chosen natural frequency (quenched disorder) and it is stirred by Brownian motion.…
We uncover a solvable generalization of the Kuramoto model in which shears (or nonisochronicities) and natural frequencies are distributed and statistically dependent. We show that the strength and sign of this dependence greatly alter…
The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…
A bifurcation from the incoherent state to the partially synchronized state of the Kuramoto-Daido model with the coupling function $f(\theta ) = \sin (\theta +\alpha _1) + h\sin 2(\theta +\alpha _2)$ is investigated based on the generalized…
The Kuramoto model of coupled second order damped oscillators on convergent sequences of graphs is analyzed in this work. The oscillators in this model have random intrinsic frequencies and interact with each other via nonlinear coupling.…
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…
When the natural frequencies are allocated symmetrically in the Kuramoto model there exists an invariant torus of dimension [N/2]+1 (N is the population size). A global phase shift invariance allows to reduce the model to $N-1$ dimensions…
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…
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…
The emergence of collective synchrony from an incoherent state is a phenomenon essentially described by the Kuramoto model. This canonical model was derived perturbatively, by applying phase reduction to an ensemble of heterogeneous,…