Optimal synchronization of Kuramoto oscillators: A dimensional reduction approach

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Rafael S Pinto, Alberto Saa

Abstract

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 ω^{T}Lω, where ω 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.

References

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Citations

Nov 3, 2017·Chaos·Georg A Gottwald
Jul 15, 2016·Physical Review. E·Markus Brede, Alexander C Kalloniatis
Oct 27, 2016·Chaos·Per Sebastian SkardalJie Sun
Aug 17, 2018·Physical Review. E·Edward J Hancock, Georg A Gottwald
Jun 17, 2018·Physical Review. E·Stefan WielandHervé Bercegol
May 16, 2018·Physical Review. E·Alberto Saa
Apr 3, 2020·Chaos·Pitambar KhanraChittaranjan Hens

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