超越成对网络的韧性
Resilience Beyond Pairwise Networks
中文总结 AI 辅助
针对含成对与高阶相互作用的单纯形复形非线性动力学，推导一维约化模型，经数值验证可复现三类系统的主要转变与稳态分支，为相关系统韧性提供易处理描述。
中文摘要 AI 辅助
我们针对包含成对及三角（高阶）相互作用的单纯形复形上的非线性动力学，推导了一维约化模型。有效状态由节点的成对度与三角度确定的混合权重定义，所得约化方程保留了分别与成对耦合通道及高阶耦合通道相关的两个结构系数。涨落展开明确了该约化模型背后的闭合假设，并阐明了各节点状态偏离有效状态的程度如何影响近似误差。我们在基因调控动力学、双势阱系统及SIS传播中对所提框架进行了数值验证，通过耦合参数扫描、稳态分支计算及合成与真实网络上的渐进节点移除实验，将约化模型的状态与全网络模拟结果进行对比。该约化模型成功复现了所考虑的三类动力学系统中的主要转变及稳态分支；在相对均匀的网络中一致性最强，当结构异质性导致节点状态分布更宽泛时一致性会下降。闭合诊断可解释这种精度损失，并明确何时单一有效状态不再适用。因此，该约化模型为同时存在成对与高阶相互作用的系统提供了一种易于处理的韧性描述。
英文摘要
We derive a one-dimensional reduction for nonlinear dynamics on simplicial complexes containing both pairwise and triangular (higher-order) interactions. The effective state is defined using a mixed weight determined by the pairwise and triangular degrees of each node. The resulting reduced equation retains two structural coefficients, associated separately with the pairwise and higher-order coupling channels. A fluctuation expansion identifies the closure assumptions underlying the reduction and shows how deviations of individual node states from the effective state contribute to the approximation error. We numerically validate the proposed framework on Gene-regulatory dynamics, the double-well system, and SIS spreading. The states of the reduced model are compared with full-network simulations through coupling-parameter sweeps, steady-state branch calculations, and progressive node-removal experiments on synthetic and real-world networks. The reduced model successfully reproduces the principal transitions and steady-state branches in all three dynamical systems considered. Agreement is strongest for relatively homogeneous networks and deteriorates when structural heterogeneity produces a broader distribution of node states. The closure diagnostics account for this loss of accuracy and indicate when a single effective state is no longer sufficient. The reduction therefore provides a tractable description of resilience in systems with coexisting pairwise and higher-order interactions.
