多交互层网络同步稳定性的平均场性质
Mean-field nature of synchronization stability in networks with multiple interaction layers
摘要：
许多现实世界系统的组件之间的交互最好由多层网络建模。已经提出了不同的理论来解释多层连接如何影响动力系统同步的线性稳定性。然而，所得到的方程在计算上是昂贵的，因此很难，如果不是不可能的话，解决大型系统。为了弥补这一差距，我们开发了一个平均场论同步网络的多个交互层。通过假设准相同的层，我们得到准确的评估同步稳定性，是可比的确切结果。事实上，我们的理论的准确性仍然很高，即使是非常不同的层的网络，从而提出了一个普遍的问题，在多层网络的同步稳定性的平均场性质。此外，我们的方法的计算复杂性只是二次的节点数，从而允许系统的研究，其调查迄今被排除在外。
英文摘要：
The interactions between the components of many real-world systems are best modelled by networks with multiple layers. Different theories have been proposed to explain how multilayered connections affect the linear stability of synchronization in dynamical systems. However, the resulting equations are computationally expensive, and therefore difficult, if not impossible, to solve for large systems. To bridge this gap, we develop a mean-field theory of synchronization for networks with multiple interaction layers. By assuming quasi-identical layers, we obtain accurate assessments of synchronization stability that are comparable with the exact results. In fact, the accuracy of our theory remains high even for networks with very dissimilar layers, thus posing a general question about the mean-field nature of synchronization stability in multilayer networks. Moreover, the computational complexity of our approach is only quadratic in the number of nodes, thereby allowing the study of systems whose investigation was thus far precluded.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
