2015/08/31 by Rafael S. Pinto, Alberto Saa · 1 citation
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Artificial intelligence #Combinatorics #Computer science #Control (management) #Control theory (sociology) #Geometry #Kuramoto model #Mathematics #Nonlinear Dynamics and Pattern Formation #Reduction (mathematics) #Slime Mold and Myxomycetes Research #Synchronization (alternating current) #Synchronization networks #Topology (electrical circuits) #nlin.AO
paper · pdf · doi:10.1103/physreve.92.062801
published as Phys. Rev. E 92, 062801 (2015) · 6 pages, 6 figures, final version to appear in PRE
arxiv created 2015/11/28 · openalex publication_date 2015/12/01 · arxiv updated 2015/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.