The Kuramoto model: A simple paradigm for synchronization phenomena

Acebrón, Juan A.; Bonilla, L. L.; Vicente, C. J. Pérez; Ritort, Fèlix; Spigler, Renato

doi:10.1103/revmodphys.77.137

Cited by 2,933 publications

(3,007 citation statements)

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“…Dynamic phenomena are ubiquitous in nature and play a key role within various contexts in sociology [3], and technology [4]. To date, the problem of how the structural properties of a network influences the convergence and stability of its synchronized states has been extensively investigated and discussed, both numerically and theoretically [5,6,7,8,9], with special attention given to networks of coupled oscillators [10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Algebraic connectivity of interdependent networks

Martı́n-Hernández

Wang

Mieghem

et al. 2014

Physica A: Statistical Mechanics and its Applications

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The algebraic connectivity µ N −1 , i.e. the second smallest eigenvalue of the Laplacian matrix, plays a crucial role in dynamic phenomena such as diffusion processes, synchronization stability, and network robustness. In this work we study the algebraic connectivity in the general context of interdependent networks, or network-of-networks (NoN). The present work shows, both analytically and numerically, how the algebraic connectivity of NoNs experiences a transition. The transition is characterized by a saturation of the algebraic connectivity upon the addition of sufficient coupling links (between the two individual networks of a NoN). In practical terms, this shows that NoN topologies require only a fraction of coupling links in order to achieve optimal diffusivity. Furthermore, we observe a footprint of the transition on the properties of Fiedler's spectral bisection.

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Section: Introductionmentioning

confidence: 99%

Algebraic connectivity of interdependent networks

Martı́n-Hernández

Wang

Mieghem

et al. 2014

Physica A: Statistical Mechanics and its Applications

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“…Previous work on the questions of oscillator synchrony in the presence of noise has mainly been applied to differential equations models (Sompolinsky et al, 1991;Tass 2003;Acebron et al, 2005;Strogatz, 2000, ). For neurons coupled in a pulsatile manner, maps are a more natural setting.…”

Section: Discussionmentioning

confidence: 99%

Phase resetting and coupling of noisy neural oscillators

Ermentrout

Saunders

2006

J Comput Neurosci

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A number of experimental groups have recently computed Phase Response Curves (PRCs) for neurons. There is a great deal of noise in the data. We apply methods from stochastic nonlinear dynamics to coupled noisy phaseresetting maps and obtain the invariant density of phase distributions. By exploiting the special structure of PRCs, we obtain some approximations for the invariant distributions. Comparisons to Monte-Carlo simulations are made. We show how phase-dependence of the noise can move the peak of the invariant density away from the peak expected from the analysis of the deterministic system and thus lead to noise-induced bifurcations.

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“…The Kuramoto model (Acebrón et al, 2005) was considered by Honey and Sporn (Honey and Sporns, 2008) for simulation of the effects of cortical lesions. This model is described in the supplementary material.…”

Section: Dynamical Processesmentioning

confidence: 99%