Related papers: Model reduction for networks of coupled oscillator…
Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…
We study the onset of synchronization in square lattices of limit cycle oscillators with long-range coupling by means of numerical simulations of the Kuramoto model. In this regime the critical coupling strength depends on the system size…
The incoherent state of the Kuramoto model of coupled oscillators exhibits marginal modes in mean field theory. We demonstrate that corrections due to finite size effects render these modes stable in the subcritical case, i.e. when the…
We present a rigorous mathematical framework establishing the equivalence of four classical notions of synchronization full phase-locking, phase-locking, frequency synchronization, and order parameter synchronization in generalized Kuramoto…
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…
We study the synchronization of a generalized Kuramoto system in which the coupling weights are determined by the phase differences between oscillators. We employ the fast-learning regime in a Hebbian-like plasticity rule so that the…
We investigate the synchronization transition of the modified Kuramoto model where the oscillators form a scale-free network with degree exponent $\lambda$. An oscillator of degree $k_i$ is coupled to its neighboring oscillators with…
The second-order Kuramoto equation describes synchronization of coupled oscillators with inertia, which occur in power grids for example. Contrary to the first-order Kuramoto equation it's synchronization transition behavior is much less…
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 with high-order coupling has recently attracted some attention in the field of coupled oscillators in order, for instance, to describe clustering phenomena in sets of coupled agents. Instead of considering interactions…
Synchronizing phase frustrated Kuramoto oscillators, a challenge that has found applications from neuronal networks to the power grid, is an eluding problem, as even small phase-lags cause the oscillators to avoid synchronization. Here we…
We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…
Synchronization in networks of coupled oscillators is a widely studied topic with extensive scientific and engineering applications. In this paper, we study the frequency synchronization problem for networks of Kuramoto oscillators with…
We analyze two classes of Kuramoto models on spheres that have been introduced in previous studies. Our analysis is restricted to ensembles of identical oscillators with the global coupling. In such a setup, with an additional assumption…
The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single…
We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant…
We consider the synchronization of oscillators in complex networks where there is an interplay between the oscillator dynamics and the network topology. Through a remarkable transformation in parameter space and the introduction of virtual…
We propose Moebius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally…
This paper used multi-scale method and KBM method to get approximate solution of coupled Van der Pol oscillators, based on which, researchers investigated the impact several parameters have on the prerequisite of synchronization and the…
Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behaviour, such as frequency synchronisation (FS) as a paradigm, in real-world networks with a finite number of oscillators.…