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. Spectral graph theory has traditionally prioritized analyzing unweighted networks with specified adjacency properties. Here, we introduce a complementary framework, providing a mathematically rigorous weighted graph construction that exactly realizes any desired spectrum. We illustrate the broad applicability of this approach by showing how designer spectra can be used to control the dynamics of various archetypal physical systems. Specifically, we demonstrate that a strategically placed gap induces generalized chimera states in Kuramoto-type oscillator networks, tunes or suppresses pattern formation in a generic Swift-Hohenberg model, and leads to persistent localization in a discrete Gross-Pitaevskii quantum network. Our approach can be generalized to design continuous band gaps through periodic extensions of finite networks.

中文翻译：

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使用设计的拉普拉斯谱对网络动力学进行功能控制

可以通过动态网络模型有效地描述从航空和互联网流量到电子和基因调节电路中信号传播的各种规模的复杂现实世界现象。在许多此类系统中，基础图拉普拉斯算子的频谱在控制物质或信息流方面起着关键作用。传统上，频谱图理论优先分析具有指定邻接属性的未加权网络。在这里，我们介绍一个补充框架，提供精确实现任何所需频谱的数学上严格的加权图构造。我们通过展示如何使用设计师的光谱来控制各种原型物理系统的动力学，来说明这种方法的广泛适用性。具体来说，我们证明了策略性放置的间隙在仓本型振荡器网络中诱导广义嵌合状态，在通用Swift-Hohenberg模型中调谐或抑制模式形成，并导致在离散Gross-Pitaevskii量子网络中的持久定位。我们的方法可以推广到通过有限网络的周期性扩展来设计连续的带隙。