We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one due to the shallowness of the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply h...

[1] F. Dörfler and F. Bullo. On the critical coupling for Kuramoto oscillators. SIAM Journal on Applied Dynamical Systems, 10(3):1070–1099, 2011 [2] F. Dörfler and F. Bullo. Synchronization and transient stability in power networks and non-uniform Kuramoto oscillators. SIAM Journal on Control and Optimization, 50(3):1616–1642, 2012 [3] F. Dörfler, M. Chertkov, and F. Bullo. Synchronization in c...

We extend recent results [50] on the existence of global phase-locked states (GPLS) in the Kuramoto model on a complete graph to the case of a complete bipartite graph. In particular, we prove that, for the Kuramoto model on a complete bipartite graph, the value of the critical coupling coefficient can be determined by solving a system of two nonlinear equations that do not depend on the coupli...

The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. Sakaguchi-Kuramoto is a generalization of the basic that considers presence phase-lag parameter in interaction, thereby making it asymmetric between oscillator pairs. Here, we...

We investigate the generalized Kuramoto model of globally coupled oscillators with inertia, in which oscillators with positive coupling strength are conformists and oscillators with negative coupling strength are contrarians. We consider the correlation between the coupling strengths of oscillators and the distributions of natural frequencies. Two different types of correlations are studied. It...

The spatial scaling law and intermittency of the V2O5 surface roughness has been investigated by atomic force microscopy. The intermittency of the height fluctuations has been checked by two different methods, first, by measuring the scaling exponent of the qth moment of height-difference fluctuations i.e. Cq = 〈|h(x1)− h(x2)|q〉, and second, by defining the generating function Z(q, N) and gener...

It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the macroscopic evolution of the systems considered. For example, an exact, closed form solution for the nonlinear time evolution of the Kuramoto problem with a Loren...

We show that there is a link between the Kuramoto paradigm and another system of synchronized oscillators, namely an electrical power distribution grid of generators and consumers. The purpose of this work is to show both the formal analogy and some practical consequences. The mapping can be made quantitative, and under some necessary approximations a class of Kuramoto-like models, those with b...

A model consisting of a mixed Kuramoto-Sivashinsky-Kortewegde Vries equation, linearly coupled to an extra linear dissipative equation has been proposed in [1] in order to describe the surface waves on multi-layered liquid films and stability criteria are discussed using wave mode analysis. In this paper, we study the linear stability of solutions to the model from the viewpoint of energy estim...

We obtain a formula for the statistical distribution of instantaneous frequencies in Kuramoto-Sakaguchi model. This work is based on Kuramoto-Sakaguchi's theory globally coupled phase oscillators, which we review full detail by discussing its assumptions and showing all steps behind derivation main results. Our stationary probability density function with complex mathematical structure, consist...