Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2006-09-25
Physica D 224, 77-89 (2006)
Physics
Condensed Matter
Disordered Systems and Neural Networks
29 pages, 9 figures, accepted for publication in Physica D, minor corrections
Scientific paper
10.1016/j.physd.2006.09.007
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.
Motter Adilson E.
Nishikawa Takashi
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