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Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential…
In this paper, we study the complete synchronization of the Kuramoto model with general network containing a spanning tree, when the initial phases are distributed in an open half circle. As lack of uniform coercivity in general digraph, in…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
Synchronization in coupled oscillators networks is a remarkable phenomenon of relevance in numerous fields. For Kuramoto oscillators the loss of synchronization is determined by a trade-off between coupling strength and oscillator…
Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of…
Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster synchronization. Here we develop the necessary…
Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics, and biology. The Kuramoto model has emerged as a…
Synchronization in systems of coupled Kuramoto oscillators may depend on their natural frequencies, coupling, and underlying networks. In this paper, we reduce the alternatives to only one by considering identical oscillators where the only…
We introduce the concept of synchronization bombs as large networks of coupled heterogeneous oscillators that operate in a bistable regime and abruptly transit from incoherence to phase-locking (or vice-versa) by adding (or removing) one or…
In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is…
We present an extended analysis, based on the dynamics towards synchronization of a system of coupled oscillators, of the hierarchy of communities in complex networks. In the synchronization process, different structures corresponding to…
Synchronization in networks of interconnected oscillators is a fascinating phenomenon that appear naturally in many independent fields of science and engineering. A substantial amount of work has been devoted to understanding all possible…
The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This raises new challenges for power system stability and design. We…
Neural coupling in both neuroscience and artificial intelligence emerges as dynamic oscillatory patterns that encode abstract concepts. To this end, we hypothesize that a deeper understanding of the neural mechanisms governing brain rhythms…
Synchronization phenomena are pervasive in biology. In neuronal networks, the mechanisms of synchronization have been extensively studied from both physiological and computational viewpoints. The functional role of synchronization has also…
Synchronization and desynchronization are the two ends on the spectrum of emergent phenomena that somehow often coexist in biological, neuronal, and physical networks. However, previous studies essentially regard their coexistence as a…
Despite the large number of studies on synchronization, the hypothesis that interactions bear a cost for involved individuals has been considered seldom. The introduction of costly interactions leads, instead, to the formulation of a…
Synchronization in networks of oscillatory units is an emergent phenomenon present in various systems, such as biological, technological, and social systems. Many real-world systems have adaptive properties, meaning that their…
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…
In this work we suggest to model the dynamics of power grids in terms of a two-layer network, and use the Italian high voltage power grid as a proof-of-principle example. The first layer in our model represents the power grid consisting of…