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Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
Explosive synchronization refers to an abrupt (first order) transition to non-zero phase order parameter in oscillatory networks, underpinned by the bistability of synchronous and asynchronous states. Growing evidence suggests that this…
The features of animal population dynamics, for instance, flocking and migration, are often synchronized for survival under large-scale climate change or perceived threats. These coherent phenomena have been explained using synchronization…
Nowadays, explosive synchronization is a well documented phenomenon occurring in networks when the node frequency and its degree are correlated. This first-order transition, which may coexists with classical synchronization, has been…
We investigate synchronization in networks of Kuramoto oscillators with inertia. More specifically, we introduce a rewiring algorithm consisting basically in a {\em hill climb} scheme in which the edges of the network are swapped in order…
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…
Adaptive dynamical networks are ubiquitous in real-world systems. This paper aims to explore the synchronization dynamics in networks of adaptive oscillators based on a paradigmatic system of adaptively coupled phase oscillators. Our…
Can synchronization properties of a network of identical oscillators in the presence of noise be improved through appropriate rewiring of its connections? What are the optimal network architectures for a given total number of connections?…
We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an…
The synchronization phenomenon is ubiquitous in nature. In ensembles of coupled oscillators, explosive synchronization is a particular type of transition to phase synchrony that is first-order as the coupling strength increases. Explosive…
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…
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of…
This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective…
We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies. Among other choices we select the grid size and topology in a way that we observe a dynamically…
Occurrence of strong or mass synchronization of a large number of neuronal populations in the brain characterizes its pathological states. In order to establish an understanding of the mechanism underlying such pathological synchronization…
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…
We study patterns of partial synchronization in a network of FitzHugh-Nagumo oscillators with empirical structural connectivity measured in human subjects. We report the spontaneous occurrence of synchronization phenomena that closely…