Related papers: Stability diagram for the forced Kuramoto model
The Kuramoto model is a canonical model for understanding phase-locking phenomenon. It is well-understood that, in the usual mean-field scaling, full phase-locking is unlikely and that it is partially phase-locked states that are important…
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to…
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…
Model reduction techniques have been widely used to study the collective behavior of globally coupled oscillators. However, most approaches assume that there are infinitely many oscillators. Here we propose a new ansatz, based on the…
We consider a finite number of coupled oscillators as an adaptation of the Kuramoto model of populations of oscillators. The synchronized solutions are characterized by an integer $m$, the winding number, and a second integer $l$.…
We consider a Kuramoto model for the dynamics of an excitable system consisting of two coupled active rotators. Depending on both the coupling strength and the noise, the two rotators can be in a synchronized or desynchronized state. The…
We study a simple model of swarmalators subject to periodic forcing and confined to move around a one-dimensional ring. This is a toy model for physical systems with a mix of sync, swarming, and forcing such as colloidal micromotors. We…
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 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…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…
Finite-size systems of Kuramoto model display intricate dynamics, especially in the presence of multi-stability where both coherent and incoherent states coexist. We investigate such scenario in globally coupled populations of Kuramoto…
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…
Real world systems comprised of coupled oscillators have the ability to exhibit spontaneous synchronization and other complex behaviors. The interplay between the underlying network topology and the emergent dynamics remains a rich area of…
We analyze a variant of a model proposed by Kuramoto, Shinomoto, and Sakaguchi for a large population of coupled oscillatory and excitable elements. Using the Ott-Antonsen ansatz, we reduce the behavior of the population to a…
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…
We consider the influence of correlated noise on the stability of synchronisation of oscillators on a general network using the Kuramoto model for coupled phases $\theta_i$. Near the fixed point $\theta_i \approx \theta_j \ \forall i,j$ the…
A knot is a circle embedded in the space. Projecting a knot on a plane, we obtain a diagram which is known as the knot diagram. The vertices of the diagram, where the curved lines are crossed, can be considered as sites occupied by…
Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the…
We explore chaos in the Kuramoto model with multimodal distributions of the natural frequencies of oscillators and provide a comprehensive description under what conditions chaos occurs. For a natural frequency distribution with $M$ peaks…
Frustrated random interactions are a key ingredient of spin glasses. From this perspective, we study the dynamics of the Kuramoto model with quenched random couplings: the simplest oscillator ensemble with fully disordered interactions. We…