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Monday 16 Sep 2019Symmetries and Cluster Synchronization in Undirected Complex Networks (Mathematics Colloquium)

Louis M. Pecora - US Naval Research Laboratory, USA

Harrison 101 14:00-15:00

Complex networks of oscillators or other dynamical systems can break down into subsets of nodes that are synchronized among each other, but not synchronized to node in other subsets. We call these subsets Clusters. For large networks finding such clusters is difficult to humanly impossible. The solution is to use computational group theory to find the symmetries of the network and, hence, the clusters. In addition, other clusters that are not formed from symmetries are also possible. Such clusters are called equitable clusters or Laplacian clusters. It turns out these are intimately related to the symmetry clusters and we can construct all of them from the original symmetry clusters making the symmetry clusters the building blocks of all synchronized clusters in undirected networks. We can also use group representation theory to derive the variational equations for the stability of the symmetry, equitable, and Laplacian clusters along with their desynchronization bifurcation modes. We have recently extended these findings to multilayered networks, which add some interesting group theory constructs to the analysis. I also show some experimental results that demonstrate the success of our analysis.

Collaborators: Francesco Sorrentino (U. New Mexico), Aaron Hagerstrom (NIST Boulder), Abu Siddique (U. New Mexico), Joe Hart (U. Maryland), Rajarshi Roy (U. Maryland), Thomas Murphy (U. Maryland)

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