Pattern Formation over Multigraphs.
Pattern Formation over Multigraphs.
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DOI：
10.1109/tnse.2017.2730261
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发表时间：
2018-01
影响因子：
6.6
通讯作者：
Arcak M
中科院分区：
文献类型：
--
作者：
Gyorgy A;Arcak M
两种最常见的图案形成机制是反应扩散系统中的图灵图案化和相邻细胞的横向抑制。在本文中，我们引入了一个广义的互连模块的动力学模型来研究模式的出现，并将上述两种机制作为特例。我们的结果不限制模块的数量或其复杂性，允许具有可能不同的互连结构的多层通信信道，并且不假设两个相连的模块之间的对称连接。仅利用子系统的静态输入/输出特性和互连矩阵的谱特性，我们刻画了齐次不动点的稳定性以及出现空间非齐次图案的充分条件。为了得到这些结果，我们依赖于图的性质以及单调系统理论的工具。作为应用实例，我们考虑了模式在神经网络、反应扩散系统和随机图上的传染过程中的应用。
Two of the most common pattern formation mechanisms are Turing-patterning in reaction-diffusion systems and lateral inhibition of neighboring cells. In this paper, we introduce a broad dynamical model of interconnected modules to study the emergence of patterns, with the above mentioned two mechanisms as special cases. Our results do not restrict the number of modules or their complexity, allow multiple layers of communication channels with possibly different interconnection structure, and do not assume symmetric connections between two connected modules. Leveraging only the static input/output properties of the subsystems and the spectral properties of the interconnection matrices, we characterize the stability of the homogeneous fixed points as well as sufficient conditions for the emergence of spatially non-homogeneous patterns. To obtain these results, we rely on properties of the graphs together with tools from monotone systems theory. As application examples, we consider patterning in neural networks, in reaction-diffusion systems, and contagion processes over random graphs.