  This paper introduces an innovative graphical analysis tool for investigating
the dynamics of Memristor Cellular Nonlinear Networks (M-CNNs) featuring
2nd-order processing elements, known as M-CNN cells. In the era of specialized
hardware catering to the demands of intelligent autonomous systems, the
integration of memristors within Cellular Nonlinear Networks (CNNs) has emerged
as a promising paradigm due to their exceptional characteristics. However, the
standard Dynamic Route Map (DRM) analysis, applicable to 1st-order systems,
fails to address the intricacies of 2nd-order M-CNN cell dynamics, as well the
2nd-order DRM (DRM2) exhibits limitations on the graphical illustration of
local dynamical properties of the M-CNN cells, e.g. state derivative's
magnitude. To address this limitation, we propose a novel integration of M-CNN
cell vector field into the cell's phase portrait, enhancing the analysis
efficacy and enabling efficient M-CNN cell design. A comprehensive exploration
of M-CNN cell dynamics is presented, showcasing the utility of the proposed
graphical tool for various scenarios, including bistable and monostable
behavior, and demonstrating its superior ability to reveal subtle variations in
cell behavior. Through this work, we offer a refined perspective on the
analysis and design of M-CNNs, paving the way for advanced applications in edge
computing and specialized hardware.
