非正规网络中的同步动力学：最优性的权衡
Synchronization dynamics in non-normal networks: the trade-off for optimality
AI总结：
本文通过将非自治耦合振子系统转化为自治系统，证明强有向网络同步鲁棒性结论具有模型无关性，并揭示非正规性会使MSF失效，从而指出网络设计需权衡非正规性与有向性。
摘要：
同步是一种重要行为，刻画了由多个相互作用单元组成的众多自然系统和人造系统。它广泛存在于从神经科学到电网等一系列应用中。此类系统之所以能够同步，是因为它们表现出复杂的耦合集合，而这些耦合由复杂网络建模。系统的动力学行为与底层网络的拓扑结构紧密交织，由此引出何种最优架构能够使同步具有鲁棒性的问题。Master Stability Function（MSF，主稳定性函数）已被提出并作为处理同步问题的通用框架得到广泛研究。利用该方法，已有研究表明，对于一类模型，强有向网络中的同步对外部扰动具有鲁棒性。在本文中，我们的方法是将耦合振子的非自治系统转化为自治系统，从而证明先前的结果不依赖于具体模型。近期发现表明，许多真实世界网络具有强有向性，因此是实现最优同步的潜在候选对象。受高度有向网络同时也具有强非正规性这一事实启发，本研究探讨非正规性问题，并指出MSF等标准技术在预测同步行为稳定性时可能失效。这些结果引出非正规性与有向性之间的权衡；在设计最优网络以增强同步鲁棒性时，应适当考虑这一权衡。
英文摘要：
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention a few. Such systems synchronize because of the complex set of coupling they exhibit, the latter being modeled by complex networks. The dynamical behavior of the system and the topology of the underlying network are strongly intertwined, raising the question of the optimal architecture that makes synchronization robust. The Master Stability Function (MSF) has been proposed and extensively studied as a generic framework to tackle synchronization problems. Using this method, it has been shown that for a class of models, synchronization in strongly directed networks is robust to external perturbations. In this paper, our approach is to transform the non-autonomous system of coupled oscillators into an autonomous one, showing that previous results are model-independent. Recent findings indicate that many real-world networks are strongly directed, being potential candidates for optimal synchronization. Inspired by the fact that highly directed networks are also strongly non-normal, in this work, we address the matter of non-normality by pointing out that standard techniques, such as the MSF, may fail in predicting the stability of synchronized behavior. These results lead to a trade-off between non-normality and directedness that should be properly considered when designing an optimal network, enhancing the robustness of synchronization.
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