Optimal synchronization of Kuramoto oscillators: a dimensional reduction approach

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 ${\omega }^{T}L\omega$, 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 re-obtained 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.

6 pages, 6 figures, final version to appear in PRE

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Cited by in corpus (11)

• Development of structural correlations and synchronization from adaptive rewiring in networks of Kuramoto oscillators
• Model reduction for Kuramoto models with complex topologies
• Optimal synchronization of directed complex networks
• Optimal phase synchronization in networks of phase-coherent chaotic oscillators
• Amplification of explosive width in complex networks
• Optimal global synchronization of partially forced Kuramoto oscillators
• Symmetries and synchronization in multilayer random networks
• Synchronization of Network-Coupled Oscillators with Uncertain Dynamics
• How to grow an oscillator network with enhanced synchronization
• Adversarial control of synchronization in complex oscillator networks
• Mean-field approach for frequency synchronization in complex networks of two oscillator types