论文标题
在有向网络上的图灵不稳定性和模式形成
Turing instability and pattern formation on directed networks
论文作者
论文摘要
由自主反应扩散方程式产生的模式形成，网络上已成为科学文献中的一个共同研究主题。在这项工作中，我们主要关注定向网络。尽管已经完成了一些工作以了解导向网络上的模式是如何出现的，但这些作品将其注意力限制在laplacian矩阵（与网络相对应）的网络上。在这里，我们解决了一个问题：“如果Laplacian矩阵不可对角线化，如何检测模式形成？”为此，我们发现还可以解决由具有非本地（全局）反应动力学的反应扩散方程系统引起的模式形成的相关问题。然后将这些结果推广到包括非自治系统以及时间网络，即允许其拓扑变化的网络。
Pattern formation, arising from systems of autonomous reaction-diffusion equations, on networks has become a common topic of study in the scientific literature. In this work we focus primarily on directed networks. Although some work prior has been done to understand how patterns arise on directed networks, these works have restricted their attentions to networks for whom the Laplacian matrix (corresponding to the network) is diagonalizable. Here, we address the question "how does one detect pattern formation if the Laplacian matrix is not diagonalizable?" To this end, we find it is useful to also address the related problem of pattern formation arising from systems of reaction-diffusion equations with non-local (global) reaction kinetics. These results are then generalized to include non-autonomous systems as well as temporal networks, i.e., networks whose topology is allowed to change in time.
