多重网络中的特征向量局域化与普适区转变：一种微扰方法
Eigenvector Localization and Universal Regime Transitions in Multiplex Networks: A Perturbative Approach
AI总结：
该研究通过微扰分析多重网络超接触矩阵的主特征向量，推导出层局域化与去局域化转变的解析条件，并扩展至一般接触过程，为理解多重传染病动力学提供了统一谱框架。
摘要：
我们研究了多重网络上基于一般接触的传染病模型中，层局域化与去局域化区域之间的转变。利用逆参与率，我们刻画了活动性如何从局限于单一层转变为扩散到整个系统的过程。通过对超接触概率矩阵的主特征向量进行一阶微扰分析，我们推导出了标记两个区域之间交叉的虚构耦合$p^*$的解析表达式。这一结果重现并解释了先前观察到的数值标度，并将其推广到易感-感染-易感模型之外的一大类基于接触的过程。我们还获得了局域化区域中非主导层的IPR的解析表达式，证实了其对耦合的幂律依赖，指数为$α=4$。最后，我们研究了非主导层与主导层之间的转变与层内活动参数$γ$的函数关系。我们的解析发现得到了动力学模拟的支持，这些模拟突出了不同区域间不同的易感性模式。总的来说，这项工作为理解多重传染病动力学中的局域化和主导性转变提供了一个统一的谱框架。
英文摘要：
We study the transition between layer-localized and delocalized regimes in a general contact-based contagion model on multiplex networks. Using the inverse participation ratio, we characterize how activity shifts from being confined to a single layer to spreading across the entire system. Through a first-order perturbative analysis of the leading eigenvector of the supra-contact probability matrix, we derive an analytical expression for the fictive coupling $p^*$ that marks the crossover between the two regimes. This result reproduces and explains previously observed numerical scalings and extends them to a broad class of contact-based processes beyond the Susceptible-Infected-Susceptible model. We also obtain an analytical expression for the IPR of the non-dominant layer in the localized regime, confirming its power-law dependence on the coupling with exponent $α=4$. Finally, we study the transition between non-dominant and dominant layers as a function of the intra-layer activity parameter $γ$. Our analytical findings are supported by dynamical simulations that highlight distinct susceptibility patterns across regimes. Altogether, this work provides a unified spectral framework for understanding localization and dominance transitions in multiplex contagion dynamics.
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