Title: Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks Show Chinese title

Title: 非线性耦合的网络上Stuart-Landau振子的同步

Abstract: The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex networks, allowing for both reciprocal or non-reciprocal links. The emergence of synchronization can be deduced by proving the linear stability of the limit cycle solution for the Stuart-Landau model; the linear coupling assumption allows for a complete analytical treatment of the problem, mostly because the linearized system turns out to be autonomous. In this work, we analyze Stuart-Landau oscillators coupled through nonlinear functions on both undirected and directed networks; synchronization now depends on the study of a non-autonomous linear system and thus novel tools are required to tackle the problem. We provide a complete analytical description of the system for some choices of the nonlinear coupling, e.g., in the resonant case. Otherwise, we develop a semi-analytical framework based on Jacobi-Anger expansion and Floquet theory, which allows us to derive precise conditions for the emergence of complete synchronization. The obtained results extend the classical theory of coupled oscillators and pave the way for future studies of nonlinear interactions in networks of oscillators and beyond. Show Chinese abstract

Abstract: 耦合的Stuart-Landau振子的动力学在同步现象的研究中起着核心作用。先前的研究集中在不同配置下的线性耦合振子，例如全连接或一般的复杂网络，允许存在相互或非相互的连接。同步的出现可以通过证明Stuart-Landau模型极限环解的线性稳定性来推导；线性耦合假设使得问题能够进行完整的解析处理，主要是因为线性化系统变成了自治的。在本工作中，我们分析了通过非线性函数在无向和有向网络中耦合的Stuart-Landau振子；现在同步依赖于非自治线性系统的研究，因此需要新的工具来解决这个问题。我们提供了对某些非线性耦合选择的系统完整解析描述，例如在共振情况下。否则，我们开发了一个基于雅可比-安格展开和Floquet理论的半解析框架，这使我们能够推导出完全同步出现的精确条件。所得结果扩展了耦合振子的经典理论，并为未来对振子网络中非线性相互作用的研究铺平了道路。