Universality in network dynamics.

Despite significant advances in characterizing the structural properties of complex networks, a mathematical framework that uncovers the universal properties of the interplay between the topology and the dynamics of complex systems continues to elude us. Here we develop a self-consistent theory of dynamical perturbations in complex systems, allowing us to systematically separate the contribution of the network topology and dynamics. The formalism covers a broad range of steady-state dynamical processes and offers testable predictions regarding the system's response to perturbations and the development of correlations. It predicts several distinct universality classes whose characteristics can be derived directly from the continuum equation governing the system's dynamics and which are validated on several canonical network-based dynamical systems, from biochemical dynamics to epidemic spreading. Finally, we collect experimental data pertaining to social and biological systems, demonstrating that we can accurately uncover their universality class even in the absence of an appropriate continuum theory that governs the system's dynamics.

尽管在表征复杂网络的结构特性方面取得了重大进展，但一个能够揭示复杂系统的拓扑结构和动力学之间相互作用的普遍特性的数学框架仍然让我们难以捉摸。在此，我们提出了一种复杂系统中动态扰动的自洽理论，使我们能够系统地分离网络拓扑结构和动力学的贡献。这种形式体系涵盖了广泛的稳态动态过程，并针对系统对扰动的响应以及相关性的发展提供了可检验的预测。它预测了几个不同的普适类，其特征可直接从控制系统动力学的连续方程推导得出，并且在从生化动力学到传染病传播的几个基于网络的典型动态系统中得到了验证。最后，我们收集了与社会和生物系统相关的实验数据，表明即使在缺乏控制系统动力学的适当连续理论的情况下，我们也能够准确地揭示它们的普适类。