Related papers: Synchronization in clustered random networks
We analyze the interplay of synchronization and structure evolution in an evolving network of phase oscillators. An initially random network is adaptively rewired according to the dynamical coherence of the oscillators, in order to enhance…
Complex networks often possess communities defined based on network connectivity. When dynamics undergo in a network, one can also consider dynamical communities; i.e., a group of nodes displaying a similar dynamical process. We have…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
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…
Real-world networks are often characterized by simultaneous interactions between multiple agents that adapt themselves due to feedback from the environment. In this article, we investigate the dynamics of an adaptive multilayer network of…
Synchronization in networks of interconnected oscillators is a fascinating phenomenon that appear naturally in many independent fields of science and engineering. A substantial amount of work has been devoted to understanding all possible…
We investigate the connection between the dynamics of synchronization and the modularity on complex networks. Simulating the Kuramoto's model in complex networks we determine patterns of meta-stability and calculate the modularity of the…
We examine the onset of synchronization transition in a star network of Kuramoto phase oscillators in the presence of inertia and a time delay in the coupling. A direct correlation between the natural frequencies of the oscillators and…
In this paper, we will study the emergent behavior of Kuramoto model with frustration on a general digraph containing a spanning tree. We provide a sufficient condition for the emergence of asymptotical synchronization if the initial data…
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…
Finding the conditions that foster synchronization in networked oscillatory systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in…
The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g. mean field models) or inactive (e.g…
Synchronization is a ubiquitous phenomenon in complex systems. The Kuramoto model serves as a paradigmatic framework for understanding how coupled oscillators achieve collective rhythm. Conventional approaches focus on pairwise…
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…
We study the emergence of synchronization in the Kuramoto model on a digraph in the presence of time delays. Assuming the digraph is strongly connected, we first establish a uniform bound on the phase diameter and subsequently prove the…
Functions of some networks, such as power grids and large-scale brain networks, rely on not only frequency synchronization, but also phase synchronization. Nevertheless, even after the oscillators reach to frequency-synchronized status,…
Brain imaging data mapping onto human connectome networks enables the investigation of global brain dynamics, where the brain hubs play an essential role in transferring activity between different brain parts. At this scale, the…
The Kuramoto model and its generalizations have been broadly employed to characterize and mechanistically understand various collective dynamical phenomena, especially the emergence of synchrony among coupled oscillators. Despite almost…
A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a…
An incorporation of higher-order interactions is known to lead an abrupt first-order transition to synchronization in otherwise smooth second-order one for pair-wise coupled systems. Here, we show that adaptation in higher-order coupling…