Pattern Formation in Complex Networks

Fluctuations are ubiquitous in real-world complex oscillatory networks. For instance, AC power grids with complex topologies are now more and more integrated with renewable energy sources such as wind power and solar power, which bring fluctuations in the power inputs and would potentially undermine the stability of the entire grid. How does such a complex oscillatory network at a stable operation state respond to an external driving signal, and how would such spatio-temporal response patterns look like?

We find that, for diffusively coupled oscillatory networks, there exist three regimes of response patterns with distinctive spatio-temporal properties: the bulk regime, the resonant regime and the localized regime (Zhang et al., Sci. Adv. 2019).