Climaco Joyce S, Saa Alberto
Department of Applied Mathematics, University of Campinas, 13083-859 Campinas, São Paulo, Brazil.
Chaos. 2019 Jul;29(7):073115. doi: 10.1063/1.5097847.
We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies ω, such that a fraction of them is subject to an external periodic force with frequency Ω, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that |ω-Ω| is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization is a desired property. Some properties of the optimal forced networks and their relation to recent results in the literature are also discussed.
我们考虑了一个大型随机库拉索振荡器网络中的全局同步问题，其中一些振荡器受到外部周期性驱动力的作用。我们探索了最近提出的降维方法，并为该问题引入了一种有效的二维描述。从降维模型中，我们获得了系统中出现全局同步状态所需的一些关键参数的解析预测。此外，低维模型还使我们能够为该问题引入一种优化方案。我们的主要结论已通过详尽的数值模拟得到证实，即对于给定的具有随机固有频率ω的大型随机库拉索振荡器网络，其中一部分受到频率为Ω的外部周期性力的作用，最佳的全局同步特性对应于选择受迫振荡器的比例，使得|ω - Ω|最大的情况。我们的结果可能会为自然系统的结构和演化提供一些启示，对于这些自然系统而言，全局同步的存在与否是一种期望的特性。还讨论了最优受迫网络的一些性质及其与文献中最新结果的关系。
