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Synchronization commonly occurs in many natural and man-made systems, from neurons in the brain to cardiac cells to power grids to Josephson junction arrays. Transitions to or out of synchrony for coupled oscillators depend on several…
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…
The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally-coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of…
We study phase locking in the Kuramoto model of coupled oscillators in the special case where the number of oscillators, $N$, is large but finite, and the oscillators' natural frequencies are evenly spaced on a given interval. In this case,…
We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean…
We study synchronization dynamics in networks of coupled oscillators with bimodal distribution of natural frequencies. This setup can be interpreted as a simple model of frequency synchronization dynamics among generators and loads working…
Kuramoto oscillators have been proposed earlier as a model for interacting systems that exhibit synchronisation. In this article we study the difference between networks with symmetric and asymmetric distribution of natural frequencies. We…
Experimental studies of synchronization properties on networks with controlled connection topology can provide powerful insights into the physics of complex networks. Here, we report experimental results on the influence of connection…
We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the…
The number $\mathcal{N}$ of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining…
In previous work, empirical evidence indicated that a time-varying network could propagate sufficient information to allow synchronization of the sometimes coupled oscillators, despite an instantaneously disconnected topology. We prove here…
We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance in power-grids where energy is either…
We consider an extension of Kuramoto's model of coupled phase oscillators where oscillator pairs interact with different strengths. When the coupling coefficient of each pair can be separated into two different factors, each one associated…
We solve a longstanding stability problem for the Kuramoto model of coupled oscillators. This system has attracted mathematical attention, in part because of its applications in fields ranging from neuroscience to condensed-matter physics,…
Higher-order interactions fundamentally shape collective dynamics in oscillator networks. The topological Kuramoto model captures these effects by extending synchronization models to include interactions between cells of arbitrary dimension…
We study synchronization of coupled Kuramoto oscillators with heterogeneous inherent frequencies and general underlying connectivity. We provide conditions on the coupling strength and the initial phases which guarantee the existence of a…
We study a system of coupled oscillators of the Sakaguchi-Kuramoto type with interactions including a phase delay. We consider the case of a coupling matrix such that oscillators with large natural frequencies drive all slower ones but not…
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…
We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we…
In this paper, we consider an $N$-oscillators complexified Kuramoto model. We first observe that there are solutions exhibiting finite-time blow-up behavior in all coupling regimes. When the coupling strength $\lambda>\lambda_c$, sufficient…