On Unstable Spatial Modes and Patterns in Cellular and Graph Neural Circuits

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.