Related papers: Bifurcations and patterns in the Kuramoto model wi…
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…
The Kuramoto model provides a prototypical framework to synchronization phenomena in interacting particle systems. Apart from full phase synchrony where all oscillators behave identically, identical Kuramoto oscillators with ring-like…
We study the synchronized behavior of the inertial Kuramoto oscillators with frustration effect under a symmetric and connected network. Due to the lack of second-order gradient flow structure and singularity of second-order derivative of…
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 problem of synchronization of coupled oscillators in a Kuramoto-type model with lossy couplings. Kuramoto models have been used to gain insight on the stability of power networks which are usually nonlinear and involve large…
The Kuramoto model has provided deep insights into synchronization phenomena and remains an important paradigm to study the dynamics of coupled oscillators. Yet, despite its success, the asynchronous regime in the Kuramoto model has…
In the context of the Kuramoto model of coupled oscillators with distributed natural frequencies interacting through a time-delayed mean-field, we derive as a function of the delay exact results for the stability boundary between the…
We study feedback control of twisted states in the Kuramoto model (KM) of identical oscillators defined on deterministic nearest neighbor graphs containing complete simple ones when it may have phase-lag. Bifurcations of such twisted…
We derive the Kuramoto model (KM) corresponding to a population of weakly coupled, nearly identical quadratic integrate-and-fire (QIF) neurons with both electrical and chemical coupling. The ratio of chemical to electrical coupling…
The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first and second order corrections…
We analyze a large system of globally coupled phase oscillators whose natural frequencies are bimodally distributed. The dynamics of this system has been the subject of long-standing interest. In 1984 Kuramoto proposed several conjectures…
We investigate the origin of frequency clusters - states where multiple groups of oscillators with distinct mean frequencies coexist. We use the Kuramoto model with inertia, where identical oscillators are globally coupled. First, we study…
We study the Hamiltonian Mean Field (HMF) model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite size…
We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical simulations we explore a special case in which…
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…
A Hopf bifurcation in the Kuramoto-Daido model is investigated based on the generalized spectral theory and the center manifold reduction for a certain class of frequency distributions. The dynamical system of the order parameter on a…
We study dynamics of phase-differences (PDs) of coupled oscillators where both the intrinsic frequencies and the couplings vary in time. In case the coupling coefficients are all nonnegative, we prove that the PDs are asymptotically stable…
We prove the existence of a multi-dimensional non-trivial invariant toroidal manifold for the Kuramoto network with adaptive coupling. The constructed invariant manifold corresponds to the multi-cluster behavior of the oscillators phases.…
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 Kuramoto model. We develop a quantitative Tikhonov theorem,…