有向网络上的Benjamin-Feir不稳定性
Benjamin-Feir instabilities on directed networks
摘要：
研究了复Ginzburg-Landau方程，假定方程为耦合振子的有向网络。这种不对称性使得拉普拉斯算子的谱变得复杂，它最终导致了一类广义拓扑不稳定性的发生，这让人想起本杰明-费尔型。分析最初进行了一个特定的网络类，其特征在于由循环邻接矩阵。这使我们能够在参数空间中解析地描绘出广义不稳定性发生的区域。然后，我们继续考虑家庭的非线性振荡器耦合通过一个通用的直接，虽然平衡，图。在一个自洽的理论框架内讨论了新兴模式的特点。
英文摘要：
The Complex Ginzburg-Landau equation is studied assuming a directed network of coupled oscillators. The asymmetry makes the spectrum of the Laplacian operator complex, and it is ultimately responsible for the onset of a generalized class of topological instability, reminiscent of the Benjamin-Feir type. The analysis is initially carried out for a specific class of networks, characterized by a circulant adjacency matrix. This allows us to delineate analytically the domain in the parameter space for which the generalized instability occurs. We then move forward to considering the family of non linear oscillators coupled via a generic direct, though balanced, graph. The characteristics of the emerging patterns are discussed within a self-consistent theoretical framework.
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