循环-星形 motif：网络对链路修改的响应
Cycle-Star Motifs: Network Response to Link Modifications
AI总结：
本文研究有向图中添加反向边对网络同步的影响，提出基于图结构和大小的准则预测谱间隙变化，发现链路添加可能阻碍集体动力学，从而改进网络控制。
摘要：
理解提高网络功能的有效修改是一个具有科学和工业意义的基本问题。我们研究了一个由两个强连通分量组成的弱连通有向图上的网络动力学对链路修改的响应：一个无向星形和一个无向循环。我们假设存在从循环出发并终止于星形的有向边（主从形式）。我们通过添加从星形出发并终止于循环的任意大权重的有向边（与割集方向相反）来修改图。我们提供了基于星形和循环的大小、耦合结构以及割集和修改边的权重的准则，以确定修改如何影响拉普拉斯矩阵的谱间隙。我们应用我们的方法来理解在混沌洛伦兹系统以及Rössler系统中增强或阻碍同步的修改。我们的结果表明，由于链路添加导致的集体动力学阻碍并非如先前修改分析所预期的那样非典型，从而允许更好地控制集体性质。
英文摘要：
Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master-slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as Rössler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.
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