Controlling Complex Network Dynamics Through Designer Band Gaps

Complex real-world phenomena across a wide range of scales, from aviation and internet traffic to signal propagation in electronic and gene regulatory circuits, can be efficiently described through dynamic network models. In many such systems, the spectrum of the underlying graph Laplacian plays a key role in controlling the matter or information flow. Traditionally, network theory has focused on analyzing the spectral properties of graph ensembles with predefined statistical adjacency characteristics. Here, we introduce a complementary framework, providing a mathematically rigorous graph construction that exactly realizes any desired spectrum. We illustrate the broad applicability of this approach by showing how designer band gaps can be used to control the dynamics of various archetypal physical systems. Specifically, we demonstrate that a strategically placed gap induces chimera states in Kuramoto-type oscillator networks, completely suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network. This suggests a path to novel band-gapped classes of transport systems, biomimetic networks, or disordered mechanical, optical and acoustic metamaterials.