Controlling Symmetries and Clustered Dynamics of Complex Networks

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 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.

Automated summary

Symmetries play a crucial role in regulating collective dynamics in complex networks, and this study focuses on controlling network symmetries and enforcing patterned states of synchronization. By perturbing the original network connectivity with minimal changes, desirable clustering of nodes can be achieved. The stability conditions of enforced patterns are derived and the method's performance is illustrated with examples relevant to various practical scenarios.