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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…
Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all…
Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here we leverage this relation to study a class of networks for which the threshold…
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…
We propose a novel model of oscillatory chains that generalizes the contour discrete model of Buslaev nets. The model offers a continuous description of conflicts in system dynamics, interpreted as interactions between neighboring…
The question under which conditions oscillators with slightly different frequencies synchronize appears in various settings. We show that synchronization can be achieved even for harmonic oscillators that are bilinearly coupled via a purely…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
This paper presents a nonlinear control framework for steering networks of coupled oscillators toward desired phase-locked configurations. Inspired by brain dynamics, where structured phase differences support cognitive functions, the focus…
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…
Synchronization is an ubiquitous phenomenon in dynamical systems of networked oscillators. While it is often a goal to achieve, in some context one would like to decrease it, e.g., although synchronization is essential to the good…
The emergence of explosive synchronization has been reported as an abrupt transition in complex networks of first-order Kuramoto oscillators. In this Letter, we demonstrate that the nodes in a second-order Kuramoto model, perform a cascade…
The celebrated Kuramoto model provides an analytically tractable framework to study spontaneous collective synchronization and comprises globally coupled limit-cycle oscillators interacting symmetrically with one another. The…
Synchronization is an essential property of engineered and natural networked dynamical systems. The Kuramoto model of nonlinear synchronization has been widely studied in applications including entrainment of clock cells in brain networks…
We study synchronization of sinusoidally coupled phase oscillators on networks with modular structure and a large number of oscillators in each community. Of particular interest is the hierarchy of local and global synchrony, i.e.,…
Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical…
We examine the design of the entrainment process for an uncountably infinite collection of coupled phase oscillators that are all subject to the same periodic driving signal. In the absence of coupling, an appropriately designed input can…
Suppose we are given a system of coupled oscillators on an unknown graph along with the trajectory of the system during some period. Can we predict whether the system will eventually synchronize? Even with a known underlying graph…
A model for synchronization of coupled Nakano's chaotic circuits is studied. The Nakano circuit consists of a simple RLC circuit with a switch voltage-depending reset rule which generates a discontinuous dynamics. Thus, the model that we…
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with…
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…