AI 中文总结
本文将主稳定性函数框架扩展至度异构、带权有向的延迟耦合网络，发现异构性与非互易性可增强同步性，并开发方法找到最大化同步稳定性的最优网络结构。
AI 中文摘要
时间延迟在物理和生物网络系统中普遍存在，对集体行为的涌现与稳定性起着关键作用。然而，现有针对延迟耦合系统同步分析的理论方法大多局限于度分布均匀的网络。本文将主稳定性函数框架扩展至一类广泛的度异构、带权且有向的延迟耦合网络。分析表明，与均匀网络（包括在非延迟系统中被认为最优的全连接网络）相比，异构网络中的同步性可得到增强。为识别最优异构结构，我们开发了一种网络优化方法，该方法能找到最大化同步稳定性的有向、边加权配置。研究结果显示，在延迟耦合网络中，异构性与非互易性是实现同步的关键资源。
英文摘要
Time delays are ubiquitous in physical and biological networked systems, playing a fundamental role in the emergence and stability of collective behavior. Yet, existing theoretical methods for synchronization analysis of delay-coupled systems are largely limited to networks with homogeneous degree distributions. Here, we extend the master stability function framework to a broad class of degree-heterogeneous, weighted, and directed delay-coupled networks. The analysis reveals that synchronization can be enhanced in heterogeneous networks compared to homogeneous ones, including all-to-all networks, which are known to be optimal in non-delayed systems. To identify optimal heterogeneous structures, we develop a network optimization method that finds directional, edge-weighted configurations maximizing synchronization stability. Our results show that, in delay-coupled networks, heterogeneity and nonreciprocity are key resources for synchronization.
