论文标题
具有多个相互作用层的简单复合物中同步的稳定性
Stability of synchronization in simplicial complexes with multiple interaction layers
论文作者
论文摘要
了解互连的高阶和多层结构之间的相互作用如何影响动态系统的同步行为是一个可行的问题，并且可能在神经元动力学等基本主题中应用。在这里，我们提供了一种全面的方法，用于分析具有许多相互作用层的简单复合物中完整同步状态的稳定性。我们表明，同步状态作为一种不变解决方案存在，并在存在一般耦合函数的情况下得出稳定同步状态的必要条件。它将众所周知的主要稳定函数方案推广到具有多个相互作用层的高阶结构。我们通过在范式Rössler振荡器和谢尔曼神经元模型的网络上使用它们来验证我们的理论结果，并证明组相互作用的存在大大改善了多层框架中的同步现象。
Understanding how the interplay between higher-order and multilayer structures of interconnections influences the synchronization behaviors of dynamical systems is a feasible problem of interest, with possible application in essential topics such as neuronal dynamics. Here, we provide a comprehensive approach for analyzing the stability of the complete synchronization state in simplicial complexes with numerous interaction layers. We show that the synchronization state exists as an invariant solution and derive the necessary condition for a stable synchronization state in presence of general coupling functions. It generalizes the well-known master stability function scheme to the higher-order structures with multiple interaction layers. We verify our theoretical results by employing them on networks of paradigmatic Rössler oscillators and Sherman neuronal models, and demonstrate that the presence of group interactions considerably improves the synchronization phenomenon in the multilayer framework.
