Synchronization is optimal in nondiagonalizable networks

2006/05/31 by Takashi Nishikawa, Adilson E. Motter · 5 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #cond-mat.stat-mech #nlin.AO #nlin.CD #q-bio.NC

paper · pdf · doi:10.1103/physreve.73.065106

published as Phys. Rev. E 73, 065106 (2006) · 4 pages, 1 figure; minor revision

openalex publication_date 2006/06/28 · arxiv created 2006/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider maximization of the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. By extending the master stability formalism to all possible network structures, we show that, unless some oscillator is linked to all the others, maximally synchronizable networks are necessarily nondiagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths. The results provide insights into hierarchical structures observed in complex networks in which synchronization is important.

Citations

• Emergence of scaling in random networks
• Enhancing complex-network synchronization
• Network synchronization, diffusion, and the paradox of heterogeneity

Cited by

• Controllability of complex networks via pinning
• El léxico disponible del catalán en Valencia: Hacia la necesaria planificación lingüística de una lengua minoritaria
• Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions
• Better synchronizability predicted by a new coupling method
• Network coordination and synchronization in a noisy environment with time delays