论文
arXiv
ComplexNetwork
中文标题
复杂性揭示宏观动力学的微观起源
English Title
Complexity Reveals the Microscopic Origins of Macroscopic Dynamics
Haoyang Qian, Beata Casiday, Gabriel Hood, Malbor Asllani
发布时间
2026/6/1 13:58:05
来源类型
preprint
语言
en
摘要
中文对照

真实的复杂系统常因大量组分间的相互作用而表现出集体相变。经典稳定性理论在谱空间中描述此类相变,其动力学由空间延展的全局本征模组织,而这些本征模的集体性掩盖了其与单个物理组分的直接关联。本文表明,经验随机网络中的结构无序可从根本上改变这一图景。此类性质诱发谱局域化,导致拉普拉斯本征模集中于少量节点上,从而形成一种模—节点对应关系:集体动力学主要由一个主导节点的局部行为及其与周围网络的有效耦合所决定。因此,稳定性特性可直接在节点空间而非仅在谱空间中加以诠释。基于这一原理,我们构建了一种节点分辨框架,可用于预测相变起始点、识别引发涌现集体行为的关键节点,并在经典模态理论失效的系统中恢复可解释性。在异质反应网络中,同一机制催生出奇异的集体态,其中不同节点子集展现出超越均匀性假设所能刻画的差异化动力学行为。我们的结果表明,复杂网络结构天然地引发谱局域化,从而揭示了宏观动力学背后的微观驱动机制。

English Original

Real complex systems often exhibit collective transitions emerging from interactions across many components. Classical stability theory describes such transitions in spectral space, where dynamics is organized by spatially extended global eigenmodes whose collective nature obscures direct association with individual physical components. Here, we show that structural disorder in empirical random networks can fundamentally alter this picture. These properties induce spectral localization, causing Laplacian modes to concentrate on small subsets of nodes and producing a mode--node correspondence in which collective dynamics becomes governed predominantly by the local behavior of a dominant node together with their effective coupling to the surrounding network. As a consequence, stability properties can be interpreted directly in node space rather than purely in spectral space. Exploiting this principle, we develop a node-resolved framework that predicts transition onsets, identifies the nodes responsible for emergent collective behavior, and restores interpretability in systems where classical modal theories fail. In heterogeneous reaction networks, the same mechanism gives rise to exotic collective states where different subsets of nodes develop distinct dynamical behaviors beyond those associated with homogeneous assumptions. Our results show that complex network structures naturally generate spectral localization, revealing the microscopic drivers of macroscopic dynamics.

元数据
arXiv2606.01735v1
来源arXiv
类型论文
抽取状态raw
关键词
ComplexNetwork
nlin.PS
nlin.AO