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Controlling symmetries and clustered dynamics of complex networks
IEEE Transactions on Network Science and Engineering ( IF 6.6 ) Pub Date : 2020-01-01 , DOI: 10.1109/tnse.2020.3037039
Lucia Valentina Gambuzza , Mattia Frasca , Francesco Sorrentino , Louis M. Pecora , Stefano Boccaletti

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.

中文翻译:

控制复杂网络的对称性和集群动力学

对称性是复杂网络的一个基本特征,因为它们调节图集体动态如何组织成集群状态。我们在这里展示了如何控制网络对称性,以及如何与以所需方式聚集的节点强制同步模式化状态。我们的方法包括通过添加新边或通过添加/删除链接并修改其权重来扰乱原始网络连接。通过解决合适的优化问题,我们进一步保证对现有拓扑所做的更改最小。针对一般情况推导了强制模式稳定性的条件,并通过范例说明了该方法的性能。
更新日期:2020-01-01
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