The Kuramoto model in complex networks

FA Rodrigues, TKDM Peron, P Ji, J Kurths - Physics Reports, 2016 - Elsevier
Synchronization of an ensemble of oscillators is an emergent phenomenon present in
several complex systems, ranging from social and physical to biological and technological …

Explosive transitions in complex networks' structure and dynamics: Percolation and synchronization

S Boccaletti, JA Almendral, S Guan, I Leyva, Z Liu… - Physics Reports, 2016 - Elsevier
Percolation and synchronization are two phase transitions that have been extensively
studied since already long ago. A classic result is that, in the vast majority of cases, these …

Explosive synchronization in adaptive and multilayer networks

X Zhang, S Boccaletti, S Guan, Z Liu - Physical review letters, 2015 - APS
At this time, explosive synchronization (ES) of networked oscillators is thought of as being
rooted in the setting of specific microscopic correlation features between the natural …

Explosive phenomena in complex networks

RM D'Souza, J Gómez-Gardenes, J Nagler… - Advances in …, 2019 - Taylor & Francis
The emergence of large-scale connectivity and synchronization are crucial to the structure,
function and failure of many complex socio-technical networks. Thus, there is great interest …

Hyperedge overlap drives explosive transitions in systems with higher-order interactions

F Malizia, S Lamata-Otín, M Frasca, V Latora… - Nature …, 2025 - nature.com
Recent studies have shown that novel collective behaviors emerge in complex systems due
to the presence of higher-order interactions. However, how the collective behavior of a …

Discontinuous transitions and rhythmic states in the D-dimensional Kuramoto model induced by a positive feedback with the global order parameter

X Dai, X Li, H Guo, D Jia, M Perc, P Manshour, Z Wang… - Physical review …, 2020 - APS
From fireflies to cardiac cells, synchronization governs important aspects of nature, and the
Kuramoto model is the staple for research in this area. We show that generalizing the model …

Explosive synchronization dependence on initial conditions: The minimal Kuramoto model

A Bayani, S Jafari, H Azarnoush, F Nazarimehr… - Chaos, Solitons & …, 2023 - Elsevier
Transitions from incoherent to coherent dynamical states can be observed in various real-
world networks, ranging from neurons to power-grids. These transitions can be explosive or …

Explosive synchronization in a general complex network

X Zhang, X Hu, J Kurths, Z Liu - Physical Review E—Statistical, Nonlinear, and …, 2013 - APS
Explosive synchronization (ES) has recently attracted much attention, where its two
necessary conditions are found to be a scale-free network topology and a positive …

Cluster explosive synchronization in complex networks

P Ji, TKDM Peron, PJ Menck, FA Rodrigues, J Kurths - Physical review letters, 2013 - APS
The emergence of explosive synchronization has been reported as an abrupt transition in
complex networks of first-order Kuramoto oscillators. In this Letter we demonstrate that the …

Restoration of rhythmicity in diffusively coupled dynamical networks

W Zou, DV Senthilkumar, R Nagao, IZ Kiss… - Nature …, 2015 - nature.com
Oscillatory behaviour is essential for proper functioning of various physical and biological
processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to …