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

TL;DR

This paper reveals that optimal network synchronization is achieved through quantized total interaction strength and the strategic use of negative interactions, challenging the idea that more connections always improve synchronization.

Contribution

It introduces a novel framework showing that networks with quantized interaction strength and negative links can optimize synchronization, extending previous metabolic network findings.

Findings

Networks with optimal synchronization have quantized total interaction strength.

Negative interactions and link removals can enhance synchronization.

Optimal networks can have arbitrary complexity with constrained total interaction.

Abstract

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.