The aim of this paper is to discuss several aspects regarding the dynamics and pattern formation in select cellular and graph neural circuit type architectures and to propose a new application. A unifying approach for these types of neural circuits based on unstable spatial modes using the mode decoupling technique is presented. The main objective of this study is that of showing the way the dynamics can be prescribed by speculating the relationship between the extended graph Laplacian and nodal equations of a specific architecture. Based on the above, the possibility of designing a so-called spatial comparator that can extract the sign of a prescribed spatial mode contained in a spatial signal, using unstable circuits for which that mode is associated with a right half-plane eigenvalue, is analyzed and illustrated with simulations in CMOS technology.

中文翻译：

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关于细胞和图神经电路中的不稳定空间模式和模式

本文的目的是讨论有关选定细胞和图形神经电路类型架构中的动力学和模式形成的几个方面，并提出一个新的应用程序。提出了一种基于不稳定空间模式的神经电路类型的统一方法，该方法使用模式解耦技术。本研究的主要目的是通过推测特定架构的扩展图拉普拉斯方程和节点方程之间的关系来显示动力学的规定方式。基于以上，设计所谓的空间比较器的可能性可以使用与右半平面特征值相关联的不稳定电路来提取空间信号中包含的指定空间模式的符号，并通过 CMOS 技术中的模拟进行分析和说明。