Related papers: Pattern selection in a ring of Kuramoto oscillator…
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial…
Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…
Synchronization systems with effective inertia, such as power grid networks and coupled electromechanical oscillators, are commonly modeled by the second-order Kuramoto model. In the forward process, numerical simulations exhibit a…
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 analyze synchronization between two interacting populations of different phase oscillators. For the important case of asymmetric coupling functions, we find a much richer dynamical behavior compared to that of symmetrically coupled…
Disorder is often seen as detrimental to collective dynamics, yet recent work has shown that heterogeneity can enhance network synchronization. However, its constructive role in stabilizing nontrivial cooperative patterns remains largely…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
Synchronization and desynchronization are the two ends on the spectrum of emergent phenomena that somehow often coexist in biological, neuronal, and physical networks. However, previous studies essentially regard their coexistence as a…
Uncertain recognition success, unfavorable scaling of connection complexity or dependence on complex external input impair the usefulness of current oscillatory neural networks for pattern recognition or restrict technical realizations to…
We analyze repulsively coupled Kuramoto oscillators, which are exposed to a distribution of natural frequencies. This source of disorder leads to closed orbits with a variety of different periods, which can be orders of magnitude longer…
We present a novel method to compute the phase space distribution in the nonequilibrium stationary state of a wide class of mean-field systems involving rotators subject to quenched disordered external drive and dissipation. The method…
We use a complex-valued transformation of the Kuramoto model to develop an operator-description of the linear stability in finite networks of nonlinear oscillators. This mathematical approach offers analytical predictions for the linear…
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,…
The Kuramoto model is a mean-field model for the synchronisation behaviour of oscillators, which exhibits Landau damping. In a recent work, the nonlinear stability of a class of spatially inhomogeneous stationary states was shown under the…
This article investigates the Kuramoto model with three oscillators that are interconnected by an isosceles triangle network. The characteristic of this model is that the coupling connections between the oscillators can be either attractive…
We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes…
The Kuramoto model is one of the most widely studied model for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization…
Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation…
We study the onset of synchronization in square lattices of limit cycle oscillators with long-range coupling by means of numerical simulations of the Kuramoto model. In this regime the critical coupling strength depends on the system size…
We show that for the Kuramoto model (with identical phase oscillators equally coupled) its global statistics and size of the basins of attraction can be estimated through the eigenvalues of all stable (frequency) synchronized states. This…