Optimal synchronization of Kuramoto oscillators : a dimensional reduction approach
Alberto Pinto Rafael S. Saa
ARTIGO
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A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase...
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A recently proposed dimensional reduction approach for studying synchronization in the Kuramoto model is employed to build optimal network topologies to favor or to suppress synchronization. The approach is based in the introduction of a collective coordinate for the time evolution of the phase locked oscillators, in the spirit of the Ott-Antonsen ansatz. We show that the optimal synchronization of a Kuramoto network demands the maximization of the quadratic function omega(T) L omega, where omega stands for the vector of the natural frequencies of the oscillators and L for the network Laplacian matrix. Many recently obtained numerical results can be reobtained analytically and in a simpler way from our maximization condition. A computationally efficient hill climb rewiring algorithm is proposed to generate networks with optimal synchronization properties. Our approach can be easily adapted to the case of the Kuramoto models with both attractive and repulsive interactions, and again many recent numerical results can be rederived in a simpler and clearer analytical manner
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CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ
COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPES
FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP
2013/09357-9
aberto
Optimal synchronization of Kuramoto oscillators : a dimensional reduction approach
Alberto Pinto Rafael S. Saa
Optimal synchronization of Kuramoto oscillators : a dimensional reduction approach
Alberto Pinto Rafael S. Saa
Fontes
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Physical review E: covering statistical, nonlinear, biological, and soft matter physics Vol. 92, no. 6 (Dec., 2015), p. 1-6, n. art. 062801 |