# The Kuramoto model in complex networks

@article{Rodrigues2015TheKM, title={The Kuramoto model in complex networks}, author={Francisco Aparecido Rodrigues and Thomas K. D. M. Peron and Peng Ji and J{\"u}rgen Kurths}, journal={arXiv: Adaptation and Self-Organizing Systems}, year={2015} }

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be… Expand

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#### 450 Citations

Model reduction for Kuramoto models with complex topologies.

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The effects of time-evolving network topology on coupled Kuramoto oscillators with inertia are studied, showing that hysteretic synchronization behavior occurs when the network density of coupled inertial oscillators is slowly varied as the dynamics evolve and that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony. Expand

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Recently introduced approaches, known as the Ott–Antonsen and Watanabe–Strogatz reductions, allowing one to simplify the analysis by bridging small and large scales are reviewed, resulting in reduced model equations that exactly describe the collective dynamics for each subpopulation in the oscillator network via few collective variables only. Expand

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This work investigates the robustness of multicluster states on networks of adaptively coupled Kuramoto-Sakaguchi oscillators against the random dilution of the underlying network topology, utilizing the master stability approach for adaptive networks in order to highlight the interplay between adaptivity and topology. Expand

Synchronization invariance under network structural transformations.

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This work derives a method based on information theory principles, that allows us to adjust the weights of the structural interactions to map random homogeneous in-degree networks into random heterogeneous networks and vice versa, keeping synchronization values invariant, and reveals an interesting principle. Expand

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This paper provides a sufficient condition under which the Kuramoto model with non-identical oscillators has one unique and stable equilibrium, and this equilibrium is phase cohesive and enjoys local exponential synchronization. Expand

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The minimum coupling strength required to ensure total frequency synchronization in a Kuramoto system, called the critical coupling, is investigated and a unified order parameter based approach is developed to create approximations of thecritical coupling. Expand

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