Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions

Details Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions

2009-09-15

arxiv.org/abs/0909.2874v2

PNAS 107, 10342-10347 (2010)

Physics

Condensed Matter

Disordered Systems and Neural Networks

11 pages and 8 figures (including Supporting Information), Supporting video available at http://www.youtube.com/watch?v=3dMI1Y

Scientific paper

10.1073/pnas.0912444107

Synchronization, in which individual dynamical units keep in pace with each other in a decentralized fashion, depends both on the dynamical units and on the properties of the interaction network. Yet, the role played by the network has resisted comprehensive characterization within the prevailing paradigm that interactions facilitating pair-wise synchronization also facilitate collective synchronization. Here we challenge this paradigm and show that networks with best complete synchronization, least coupling cost, and maximum dynamical robustness, have arbitrary complexity but quantized total interaction strength that constrains the allowed number of connections. It stems from this characterization that negative interactions as well as link removals can be used to systematically improve and optimize synchronization properties in both directed and undirected networks. These results extend the recently discovered compensatory perturbations in metabolic networks to the realm of oscillator networks and demonstrate why "less can be more" in network synchronization.

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