标题： 探索在圆环拓扑上的 Kuramoto 模型中兴奋性和抑制性相互作用的相互作用 显示英文标题

标题： Exploring the Interplay of Excitatory and Inhibitory Interactions in the Kuramoto Model on Circle Topologies

摘要： 在集体动力学领域，Kuramoto 模型是研究同步现象的基准模型。 虽然平均场方法和复杂网络已经被广泛研究，但圆环的简单拓扑结构仍然相对未被探索，尤其是在兴奋性和抑制性相互作用的背景下。 在本工作中，我们关注具有正负连接的圆环上的 Kuramoto 模型的动力学，注意到了不同于同步状态的新吸引子的存在。 通过分析和计算方法，我们发现即使对于相同的振荡器，引入抑制性相互作用也会显著改变系统的吸引子结构。 我们的结果扩展了对简单拓扑中同步性的当前理解，并为物理系统中集体动力学的研究开辟了新途径。 显示英文摘要

摘要： In the field of collective dynamics, the Kuramoto model serves as a benchmark for the investigation of synchronization phenomena. While mean-field approaches and complex networks have been widely studied, the simple topology of a circle is still relatively unexplored, especially in the context of excitatory and inhibitory interactions. In this work, we focus on the dynamics of the Kuramoto model on a circle with positive and negative connections paying attention to the existence of new attractors different from the synchronized state. Using analytical and computational methods, we find that even for identical oscillators, the introduction of inhibitory interactions significantly modifies the structure of the attractors of the system. Our results extend the current understanding of synchronization in simple topologies and open new avenues for the study of collective dynamics in physical systems.