Maximum performance at minimum cost in network synchronization

By Takashi Nishikawa, Adilson E. Motter. 2006

140 citations recorded by the source corpus.

We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the case of non-diagonalizable Laplacian matrices. We then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the Laplacian eigenvalues. Among the optimal networks, we identify a subclass of hierarchical networks, characterized by the absence of feedback loops and the normalization of inputs. We show that most optimal networks are directed and non-diagonalizable, necessitating the extension of the framework. We also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints. Our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role.

Subfields: Computer Networks and Communications, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/f5a14706b997355d28c056104db804e6f5dc0a85

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Citations in the corpus

Synchronization in complex networks (2008, background): “In [96] it is proven that for any network”
Vital nodes identification in complex networks (2016, methodology): “The merit of such algorithms is to transfer the global constrains in FVS problem to local constrains in constructing the legal list L, which is also very similar to the constrains for extracting the spanning trees with maximal synchronizability [229, 230, 231].”
Global synchronization of complex dynamical networks with network failures (2010, methodology): “Based on the work of Nishikawa and Motter [5], Wu and Jiao [6] studied the synchronizability of CDNs with nonsymmetric coupling by utilizing the Jordan canonical transformation method.”