论文标题
用规定的laplacian光谱生成定向网络
Generating directed networks with prescribed Laplacian spectra
论文作者
论文摘要
复杂的现实世界现象通常被建模为网络上的动态系统。在许多感兴趣的情况下，底层图Laplacian的频谱设定了系统稳定性，并最终塑造了物质或信息流。这激发了制定合适的策略，并具有严格的数学基础，以产生具有规定光谱的Laplacian。在本文中，我们表明可以构建加权的拉普拉斯人，以确切地实现所需的复杂频谱。该方法将假定光谱是真实的现有配方的非微不足道概括。讨论了提出的技术在（i）Stuart-Landau振荡器和（ii）网络中的应用。可以通过假设正确设计，签名和加权的邻接矩阵来实现同步，以规则配对相互作用的模式。
Complex real-world phenomena are often modeled as dynamical systems on networks. In many cases of interest, the spectrum of the underlying graph Laplacian sets the system stability and ultimately shapes the matter or information flow. This motivates devising suitable strategies, with rigorous mathematical foundation, to generate Laplacian that possess prescribed spectra. In this paper, we show that a weighted Laplacians can be constructed so as to exactly realize a desired complex spectrum. The method configures as a non trivial generalization of existing recipes which assume the spectra to be real. Applications of the proposed technique to (i) a network of Stuart-Landau oscillators and (ii) to the Kuramoto model are discussed. Synchronization can be enforced by assuming a properly engineered, signed and weighted, adjacency matrix to rule the pattern of pairing interactions.
