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The Kuramoto model in complex networks
Synchronization of an ensemble of oscillators is an emergent phenomenon present in
several complex systems, ranging from social and physical to biological and technological …
several complex systems, ranging from social and physical to biological and technological …
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters, and their
complex architectures results in a variety of critical effects dramatically different from those in …
complex architectures results in a variety of critical effects dramatically different from those in …
Ralph Kenna's scaling relations in critical phenomena
In this note, we revisit the scaling relations among “hatted critical exponents”, which were
first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an …
first derived by Ralph Kenna, Des Johnston, and Wolfhard Janke, and we propose an …
Finite-size effect in Kuramoto oscillators with higher-order interactions
Finite-size systems of a Kuramoto model display intricate dynamics, especially in the
presence of multi-stability where both coherent and incoherent states coexist. We investigate …
presence of multi-stability where both coherent and incoherent states coexist. We investigate …
Finite-size scaling, dynamic fluctuations, and hyperscaling relation in the Kuramoto model
We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter
and its dynamic fluctuations near the onset of the synchronization transition, paying …
and its dynamic fluctuations near the onset of the synchronization transition, paying …
Emergent behaviour of a generalized Viscek-type flocking model
We present a planar agent-based flocking model with a distance-dependent communication
weight. We derive a sufficient condition for the asymptotic flocking in terms of the initial …
weight. We derive a sufficient condition for the asymptotic flocking in terms of the initial …
Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations
An explosive synchronization can be observed in scale-free networks when Kuramoto
oscillators have natural frequencies equal to their number of connections. The present paper …
oscillators have natural frequencies equal to their number of connections. The present paper …
Criterion for the emergence of explosive synchronization transitions in networks of phase oscillators
The emergence of explosive synchronization transitions in networks of phase oscillators
recently has become one of the most interesting topics. It is widely believed that the large …
recently has become one of the most interesting topics. It is widely believed that the large …
Transition to collective oscillations in finite Kuramoto ensembles
We present an alternative approach to finite-size effects around the synchronization
transition in the standard Kuramoto model. Our main focus lies on the conditions under …
transition in the standard Kuramoto model. Our main focus lies on the conditions under …
Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks
We study the impact of network heterogeneity on relaxation dynamics of the Kuramoto
model on uncorrelated complex networks with scale-free degree distributions. Using the Ott …
model on uncorrelated complex networks with scale-free degree distributions. Using the Ott …