This paper introduces an innovative graphical anal-ysis tool for investigating the dynamics of Memristor Cellular Nonlinear Networks (M-CNNs) featuring 2^nd-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 1^st-order systems, fails to address the intricacies of 2^nd -order M-CNN cell dynamics, as well the 2^nd-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.