Related papers: Kuramoto model with stochastic resetting and coupl…
Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
We examine analytically and numerically a variant of the stochastic Kuramoto model for phase oscillators coupled on a general network. Two populations of phased oscillators are considered, labelled `Blue' and `Red', each with their…
We demonstrate the application of the circular cumulant approach for thermodynamically large populations of phase elements, where the Ott-Antonsen properties are violated by a multiplicative intrinsic noise. The infinite cumulant equation…
Synchronization of non-identical oscillators coupled through complex networks is an important example of collective behavior. It is interesting to ask how the structural organization of network interactions influences this process. Several…
Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model…
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…
A fundamental understanding of synchronized behavior in multi-agent systems can be acquired by studying analytically tractable Kuramoto models. However, such models typically diverge from many real systems whose dynamics evolve under…
By means of numerical analysis conducted with the aid of the computer, the collective synchronization of coupled phase oscillators in the Kuramoto model in the connected regime of random networks of various sizes is studied. The oscillators…
Kuramoto model is one of the most prominent models for the synchronization of coupled oscillators. It has long been a research hotspot to understand how natural frequencies, the interaction between oscillators, and network topology…
We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction $p$ of oscillators are positively coupled, attracting all others, while the remaining fraction…
We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian…
The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…
A generalized Kuramoto model of coupled phase oscillators with slowly varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs of oscillators in such a way that the coupling…
We develop an approach for the description of the dynamics of large populations of phase oscillators based on "circular cumulants" instead of the Kuramoto-Daido order parameters. In the thermodynamic limit, these variables yield a simple…
We have studied the dynamics of the paradigmatic Kuramoto-Sakaguchi model of identical coupled phase oscilla- tors with various kinds of time-dependent connectivity using Eulerian discretization. We first explore the parameter spaces for…
We analyze accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations are considered: (i) the Ott-Antonsen ansatz, (ii) the…
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 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…
The Kuramoto model is a paradigmatic tool for studying the dynamics of collective behavior in large ensembles of coupled dynamical systems. Over the past decade a great deal of progress has been made in analytical descriptions of the…