标题： 循环-星型基序：网络对链接修改的响应 显示英文标题

标题： Cycle-Star Motifs: Network Response to Link Modifications

摘要： 理解对网络功能进行有效修改以提高其性能是一个具有科学和工业兴趣的基本问题。 我们研究在由两个强连通分量组成的弱连通有向图上的网络动态响应：一个无向星形结构和一个无向环。 我们假设存在从环出发并终止于星形的有向边（主-从形式）。 我们通过从星形出发并终止于环的任意大权重的有向边来修改图（与割集方向相反）。 我们提供了判断标准（基于星形和环的大小、耦合结构以及割集和修改边的权重），这些标准决定了修改如何影响拉普拉斯矩阵的谱间隙。 我们将我们的方法应用于理解那些增强或阻碍混沌洛伦兹系统以及罗斯勒系统网络同步的修改。 我们的结果表明，由于链接添加而导致的集体动力学阻碍并不像之前修改分析所预期的那样不常见，因此允许更好地控制集体属性。 显示英文摘要

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 R\"ossler. 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.