Complete characterization of the stability of cluster synchronization in complex dynamical networks

Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clu...

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Bibliographic Details
Published in:Science advances 2016-04, Vol.2 (4), p.e1501737-e1501737
Main Authors: Sorrentino, Francesco, Pecora, Louis M, Hagerstrom, Aaron M, Murphy, Thomas E, Roy, Rajarshi
Format: Article
Language:English
Subjects:
Computer Systems
Electricity
Models, Theoretical
Network Science
Neural Networks (Computer)
Nonlinear Dynamics
Physics
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Summary:Synchronization is an important and prevalent phenomenon in natural and engineered systems. In many dynamical networks, the coupling is balanced or adjusted to admit global synchronization, a condition called Laplacian coupling. Many networks exhibit incomplete synchronization, where two or more clusters of synchronization persist, and computational group theory has recently proved to be valuable in discovering these cluster states based on the topology of the network. In the important case of Laplacian coupling, additional synchronization patterns can exist that would not be predicted from the group theory analysis alone. Understanding how and when clusters form, merge, and persist is essential for understanding collective dynamics, synchronization, and failure mechanisms of complex networks such as electric power grids, distributed control networks, and autonomous swarming vehicles. We describe a method to find and analyze all of the possible cluster synchronization patterns in a Laplacian-coupled network, by applying methods of computational group theory to dynamically equivalent networks. We present a general technique to evaluate the stability of each of the dynamically valid cluster synchronization patterns. Our results are validated in an optoelectronic experiment on a five-node network that confirms the synchronization patterns predicted by the theory.
ISSN:2375-2548
2375-2548
DOI:10.1126/sciadv.1501737