论文标题
控制复杂网络的对称性和聚类动力学
Controlling symmetries and clustered dynamics of complex networks
论文作者
论文摘要
对称性是复杂网络的基本特征，因为它们将图形集体动力学如何组织为群集状态。我们在这里展示了如何控制网络对称性，以及如何以所需的方式强制与节点同步的模式状态。我们的方法包括通过添加新边缘或添加/删除链接以及修改其权重来扰动原始网络连接。通过解决合适的优化问题，我们进一步保证对现有拓扑的变化是最小的。为总体情况得出了强制模式稳定性的条件，该方法的性能通过范式示例进行了说明。我们的结果与所有实际情况有关，在各种情况下，将网络系统协调为不同的组可能是可取的，例如机器人团队，无人自动驾驶的车辆，电网和中央模式生成器。
Symmetries are an essential feature of complex networks as they regulate how the graph collective dynamics organizes into clustered states. We here show how to control network symmetries, and how to enforce patterned states of synchronization with nodes clustered in a desired way. Our approach consists of perturbing the original network connectivity, either by adding new edges or by adding/removing links together with modifying their weights. By solving suitable optimization problems, we furthermore guarantee that changes made on the existing topology are minimal. The conditions for the stability of the enforced pattern are derived for the general case, and the performance of the method is illustrated with paradigmatic examples. Our results are relevant to all the practical situations in which coordination of the networked systems into diverse groups may be desirable, such as for teams of robots, unmanned autonomous vehicles, power grids and central pattern generators.
