Synchronization is optimal in non-diagonalizable networks

Details Synchronization is optimal in non-diagonalizable networks Synchronization is optimal in non-diagonalizable networks

2006-05-25

arxiv.org/abs/cond-mat/0605619v2

Phys. Rev. E 73, 065106 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 1 figure; minor revision

Scientific paper

10.1103/PhysRevE.73.065106

We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of non-diagonalizable networks. We then show that, unless some oscillator is connected to all the others, networks of maximum synchronizability are necessarily non-diagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths. The extension makes the formalism applicable to all possible network structures, while the maximization results provide insights into hierarchical structures observed in complex networks in which synchronization plays a significant role.

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