Related papers: Synchronization on star graph with noise
We consider the Kuramoto model on sparse random networks such as the Erd\H{o}s-R\'enyi graph or its combination with a regular two-dimensional lattice and study the dynamical scaling behavior of the model at the synchronization transition…
In this paper we explore the emergence of explosive synchronization (ES) in a star network by considering the dynamics of coupled phase oscillators in the presence of noise. While ES has been the subject of many recent studies, in most…
The transition to synchrony in the Kuramoto model of globally coupled phase oscillators with a uniform distribution of natural frequencies is discontinuous. We extend the theory of this transition to the Kuramoto-Sakaguchi model, taking…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
We tackle the quantification of synchrony in globally coupled populations. Furthermore, we treat the problem of incomplete observations when the population mean field is unavailable, but only a small subset of units is observed. We…
We investigate the dynamics of large, globally-coupled systems of Kuramoto oscillators with heterogeneous interaction delays. For the case of exponentially distributed time delays we derive the full stability diagram that describes the…
A modified Kuramoto model of synchronization in a finite discrete system of locally coupled oscillators is studied. The model consists of N oscillators with random natural frequencies arranged on a ring. It is shown analytically and…
In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter $K_c$. We obtain the asymptotic…
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…
The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto…
The Kuramoto model is the paradigmatic model to study synchronization in coupled oscillator systems. In its classical formulation, the oscillators move on the unit circle, each characterized by a scalar phase and a natural frequency, by…
We study the phase synchronization of Kuramoto's oscillators in small parts of networks known as motifs. We first report on the system dynamics for the case of a scale-free network and show the existence of a non-trivial critical point. We…
The Kuramoto model with higher-order interactions has recently been shown to exhibit bistability, explosive synchronization transitions, and rich collective dynamics. Existing analytical approaches, however, typically rely on all-to-all…
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…
A family of stochastic processes has quasi-cycle oscillations if the oscillations are sustained by noise. For such a family we define a Kuramoto-type coupling of both phase and amplitude processes. We find that synchronization, as measured…
An analysis of transition from chaotic to nonchaotic behavior and synchronization in an ensemble of systems driven by identical random forces is presented. The synchronization phenomenon is investigated in the ensemble of particles moving…
Using the Penrose method of instability analysis, we consider the synchronization transition in the Kuramoto model with inertia and noise with all-to-all couplings. Analyzing the Penrose curves, we identify the appearance of cluster and…
Imagine a group of oscillators, each endowed with their own rhythm or frequency, be it the ticking of a biological clock, the swing of a pendulum, or the glowing of fireflies. While these individual oscillators may seem independent of one…
Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and…
Synchronization in the networks of coupled oscillators is a widely studied topic in different areas. It is well-known that synchronization occurs if the connectivity of the network dominates heterogeneity of the oscillators. Despite…