Related papers: Model reduction for Kuramoto models with complex t…
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…
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…
Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…
The Kuramoto model describes the synchronization of coupled oscillators that have different natural frequencies. Among the many generalizations of the original model, Kuramoto and Sakaguchi (KS) proposed a {\it frustrated} version that…
Nature is pervaded with oscillatory dynamics. In networks of coupled oscillators patterns can arise when the system synchronizes to an external input. Hence, these networks provide processing and memory of input. We present a universal…
In this paper we address two questions about the synchronization of coupled oscillators in the Kuramoto model with all-to-all coupling. In the first part we use some classical results in convex geometry to prove bounds on the size of the…
Synchronization is a fundamental phenomenon in complex systems, observed across a wide range of natural and engineered contexts. The Kuramoto model provides a foundational framework for understanding synchronization among coupled…
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…
The Kuramoto model for an ensemble of coupled oscillators provides a paradigmatic example of non-equilibrium transitions between an incoherent and a synchronized state. Here we analyze populations of almost identical oscillators in…
The Kuramoto model is a classical nonlinear ODE system designed to study synchronization phenomena. Each equation represents the phase of an oscillator and the coupling between them is determined by a graph. There is an increasing interest…
We study the synchronisation properties of the Kuramoto model of coupled phase oscillators on a general network. Here we distinguish the ability of such a system to self-synchronise from the stability of this behaviour. While…
In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…
The dynamics of large systems of coupled oscillators is a subject of increasing importance with prominent applications in several areas such as physics and biology. The Kuramoto model, where a set of oscillators move around a circle…
The classical Kuramoto model consists of finitely many pairwise coupled oscillators on the circle. In many applications a simple pairwise coupling is not sufficient to describe real-world phenomena as higher-order (or group) interactions…
An interesting problem in synchronization is the study of coupled oscillators, wherein oscillators with different natural frequencies synchronize to a common frequency and equilibrium phase difference. In this paper, we investigate the…
Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models,…
In this paper, by extending the concept of Kuramoto oscillator to the left-invariant flow on general Lie group, we investigate the generalized phase synchronization on networks. The analyses and simulations of some typical dynamical systems…
Motivated by recent interest for multi-agent systems and smart power grid architectures, we discuss the synchronization problem for the network-reduced model of a power system with non-trivial transfer conductances. Our key insight is to…
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…
We establish a unified synchronization framework for the all-to-all hybrid Kuramoto model that couples first- and second-order oscillators within a single dynamical system. Although the Kuramoto model has become one of the most widely used…