Maximum performance at minimum cost in network synchronization

PHYSICA D-NONLINEAR PHENOMENA

卷:224

Article

Nishikawa, Takashi ; Motter, Adilson E.

关键词: complex networks;    synchronization;    optimization;   

DOI  :  10.1016/j.physd.2006.09.007

来源: Elsevier

【 摘 要 】

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. (c) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free