相关论文: Counting equilibria of the Kuramoto model using bi…

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…

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 sectoral synchronization observed for the Japanese business cycle in the Indices of Industrial Production data is an example of synchronization. The stability of this synchronization under a shock, e.g., fluctuation of supply or demand,…

Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…

Based on a local greedy numerical algorithm, we compute the topology of weighted, directed, and of unlimited extension networks of non identical Kuramoto oscillators which simultaneously satisfy 2 criteria: i) global frequency…

Higher order interactions can lead to new equilibrium states and bifurcations in systems of coupled oscillators described by the Kuramoto model. However, even in the simplest case of 3-body interactions there are more than one possible…

A paradigmatic framework to study the phenomenon of spontaneous collective synchronization is provided by the Kuramoto model comprising a large collection of limit-cycle oscillators of distributed frequencies that are globally coupled…

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is in particular for real-world systems still elusive. We study the synchronization transition in a phase oscillator system with two…

The Kuramoto model is a standard model for the dynamics of coupled oscillator networks. In particular, it is used to study long time behavior such as phase-locking where all oscillators rotate at a common frequency with fixed angle…

We consider the Kuramoto model of coupled oscillators, specifically the case of tree networks, for which we prove a simple closed-form expression for the critical coupling. For several classes of tree, and for both uniform and Gaussian…

The Kuramoto model is a versatile mathematical framework that explains phenomena resulting from interactions among phase oscillators. It finds applications in various scientific and engineering domains. In this study, we focused on a…

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…

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…

The Kuramoto model of coupled second order damped oscillators on convergent sequences of graphs is analyzed in this work. The oscillators in this model have random intrinsic frequencies and interact with each other via nonlinear coupling.…

Recently, Antonioni and Cardillo proposed a coevolutionary model based on the intertwining of oscillator synchronization and evolutionary game theory [Phys. Rev. Lett. \textbf{118}, 238301 (2017)], in which each Kuramoto oscillator can…

In the context of the celebrated Kuramoto model of globally-coupled phase oscillators of distributed natural frequencies, which serves as a paradigm to investigate spontaneous collective synchronization in many-body interacting systems, we…

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…

The Kuramoto model is a system of nonlinear differential equations that models networks of coupled oscillators and is often used to study synchronization among the oscillators. In this paper we study steady state solutions of the Kuramoto…

The Kuramoto model captures various synchronization phenomena in biological and man-made systems of coupled oscillators. It is well-known that there exists a critical coupling strength among the oscillators at which a phase transition from…

In this paper we study synchronization of random clustered networks consisting of Kuramoto oscillators. More specifically, by developing a mean-field analysis, we find that the presence of cycles of order three does not play an important…